TODAY IN ALGEBRA 2.0… Warm Up: Zeros in Factored Form Learning Goal 1: 4.4 You will solve quadratics in factored form.
Download ReportTranscript TODAY IN ALGEBRA 2.0… Warm Up: Zeros in Factored Form Learning Goal 1: 4.4 You will solve quadratics in factored form.
Slide 1
TODAY IN ALGEBRA 2.0…
Warm Up: Zeros in Factored Form
Learning Goal 1: 4.4 You will solve
quadratics in factored form.
Independent Practice
WARM UP: Factor then solve the following quadratic
equations.
1. 𝑥 2 − 16𝑥 + 64 = 0
64
∗
−𝟖 −𝟖
+
−16
𝑥−8 𝑥−8 =0
𝑥−8 =0
+8 + 8
𝒙=𝟖
𝑥−8 =0
+8 + 8
𝒙=𝟖
2. 𝑥 2 − 11𝑥 + 30 = 0
30
∗
−𝟓 −𝟔
+
−11
𝑥−5 𝑥−6 =0
𝑥−5 =0
+5 + 5
𝒙=𝟓
𝑥−6 =0
+6 + 6
𝒙=𝟔
REMEMBER WHY FACTORED FORM IS IMPORTANT…
Below is the graph 𝑦 = 𝑥 2 + 2𝑥 − 8
ZEROS: Where the graph goes
through the x-axis
𝑥 = −4 𝑥 = 2
We can rewrite the equation
using the zeros:
𝑦 = 𝑥 2 + 2𝑥 − 8
𝑦 = (𝑥 + 4)(𝑥 − 2)
This is what you called
FACTORED FORM.
*Notice the signs inside the
parenthesis are opposite…
4.4 FACTORING QUADRATICS IN STANDARD FORM
TRINOMIAL FACTORING RULES:
If
𝑎𝑥 2 + 𝑏𝑥 + 𝑐
then ( +
)( +
If
𝑎𝑥 2 − 𝑏𝑥 + 𝑐
then ( −
)( −
Factored form have
the same signs.
)
If
𝑎𝑥 2 + 𝑏𝑥 − 𝑐
then ( +
)( −
)
)
If
𝑎𝑥 2 − 𝑏𝑥 − 𝑐
then ( +
)( −
)
Factored form have
the different signs.
4.4 FACTORING QUADRATICS IN STANDARD FORM
EXAMPLE: Factor then solve the following quadratic
equations.
1. 6𝑥 2 − 7𝑥 + 2 = 0
2. 3𝑥 2 + 5𝑥 − 8 = 0
3𝑥 + 8
3𝑥 − 2
= 5𝑥
= −7𝑥
𝑥 3𝑥 2 8𝑥
2𝑥 6𝑥 2 −4𝑥
−
−
1 −3𝑥 −8
1 −3𝑥 2
3𝑥 − 2 2𝑥 − 1 = 0
3𝑥 − 2 = 0 2𝑥 − 1 = 0
+1 + 1
+2 + 2
2𝑥 = 1
5𝑥 = 2
2
2
5
5
𝟏
𝟐
𝒙=
𝒙=
𝟓
𝟐
3𝑥 + 8 𝑥 − 1 = 0
3𝑥 + 8 = 0
𝑥−1 =0
−8 − 8
+1 + 1
3𝑥 = −8
𝒙=𝟏
3
3
𝟖
𝒙=−
𝟑
4.4 FACTORING QUADRATICS IN STANDARD FORM
EXAMPLE: Factor then solve the following quadratic
equations.
1. 5𝑥 2 − 17𝑥 + 6 = 0
2. 3𝑥 2 + 20𝑥 − 7 = 0
𝑥 + 7
5𝑥 − 2
= 20𝑥
= −17𝑥
3𝑥 3𝑥 2 21𝑥
𝑥 5𝑥 2 −2𝑥
−
−
1 −1𝑥 −7
3 −15𝑥 6
5𝑥 − 2 𝑥 − 3 = 0
5𝑥 − 2 = 0
𝑥−3 =0
+2 + 2
+3 + 3
5𝑥 = 2
𝒙=𝟑
5
5
𝟐
𝒙=
𝟓
3𝑥 − 1 𝑥 + 7 = 0
3𝑥 − 1 = 0
𝑥+7 =0
+1 + 1
−7 − 7
3𝑥 = 1
𝒙 = −𝟕
3
3
𝟏
𝒙=
𝟑
4.4 FACTORING QUADRATICS IN STANDARD FORM
EXAMPLE: Factor then solve the following quadratic
equations.
1. 2𝑥 2 + 11𝑥 + 12 = 0
2. 3𝑥 2 − 10𝑥 − 8 = 0
3𝑥 + 2
2𝑥 + 3
= −10𝑥
= 11𝑥
𝑥 3𝑥 2 2𝑥
𝑥 2𝑥 2 3𝑥
−
+
12
4 −12𝑥 −8
4 8𝑥
2𝑥 + 3 𝑥 + 4 = 0
2𝑥 + 3 = 0
𝑥+4 =0
−3 − 3
−4 − 4
2𝑥 = −3
𝒙 = −𝟒
2
2
𝟑
𝒙=−
𝟐
3𝑥 + 2 𝑥 − 4 = 0
3𝑥 + 2 = 0
𝑥−4 =0
−2 − 2
+4 + 4
3𝑥 = −2
𝒙=𝟒
3
3
𝟐
𝒙=−
𝟑
4.4 FACTORING QUADRATICS IN STANDARD FORM
EXAMPLE: Factor then solve the following quadratic
equations.
1. 15𝑥 2 − 2𝑥 − 8 = 0
2. 9𝑥 2 − 13𝑥 − 10 = 0
9𝑥 + 5
3𝑥 + 2
= −13𝑥
= −2𝑥
5𝑥 15𝑥 2 10𝑥
𝑥 9𝑥 2 5𝑥
−
−
2 −18𝑥 −10
4 −12𝑥 −8
3𝑥 + 2 5𝑥 − 4 = 0
3𝑥 + 2 = 0 5𝑥 − 4 = 0
−2 − 2
+4 + 4
3𝑥 = −2
5𝑥 = 4
3
3
5
5
𝟐
𝟒
𝒙=−
𝒙=
𝟑
𝟓
9𝑥 + 5 𝑥 − 2 = 0
9𝑥 + 5 = 0
𝑥−2 =0
−5 − 5
+2 + 2
9𝑥 = −5
𝒙=𝟐
9
9
𝒙=
𝟓
−
𝟗
IN CLASS WORK #4:
Solving Quadratics in Factored Form
Previous Assignments:
#1: Graphing Quadratics in Standard Form WS #1
#2: Graphing Quadratics in Vertex Form WS #2
#3: Solving Quadratics in Factored From WS #3
Slide 2
TODAY IN ALGEBRA 2.0…
Warm Up: Zeros in Factored Form
Learning Goal 1: 4.4 You will solve
quadratics in factored form.
Independent Practice
WARM UP: Factor then solve the following quadratic
equations.
1. 𝑥 2 − 16𝑥 + 64 = 0
64
∗
−𝟖 −𝟖
+
−16
𝑥−8 𝑥−8 =0
𝑥−8 =0
+8 + 8
𝒙=𝟖
𝑥−8 =0
+8 + 8
𝒙=𝟖
2. 𝑥 2 − 11𝑥 + 30 = 0
30
∗
−𝟓 −𝟔
+
−11
𝑥−5 𝑥−6 =0
𝑥−5 =0
+5 + 5
𝒙=𝟓
𝑥−6 =0
+6 + 6
𝒙=𝟔
REMEMBER WHY FACTORED FORM IS IMPORTANT…
Below is the graph 𝑦 = 𝑥 2 + 2𝑥 − 8
ZEROS: Where the graph goes
through the x-axis
𝑥 = −4 𝑥 = 2
We can rewrite the equation
using the zeros:
𝑦 = 𝑥 2 + 2𝑥 − 8
𝑦 = (𝑥 + 4)(𝑥 − 2)
This is what you called
FACTORED FORM.
*Notice the signs inside the
parenthesis are opposite…
4.4 FACTORING QUADRATICS IN STANDARD FORM
TRINOMIAL FACTORING RULES:
If
𝑎𝑥 2 + 𝑏𝑥 + 𝑐
then ( +
)( +
If
𝑎𝑥 2 − 𝑏𝑥 + 𝑐
then ( −
)( −
Factored form have
the same signs.
)
If
𝑎𝑥 2 + 𝑏𝑥 − 𝑐
then ( +
)( −
)
)
If
𝑎𝑥 2 − 𝑏𝑥 − 𝑐
then ( +
)( −
)
Factored form have
the different signs.
4.4 FACTORING QUADRATICS IN STANDARD FORM
EXAMPLE: Factor then solve the following quadratic
equations.
1. 6𝑥 2 − 7𝑥 + 2 = 0
2. 3𝑥 2 + 5𝑥 − 8 = 0
3𝑥 + 8
3𝑥 − 2
= 5𝑥
= −7𝑥
𝑥 3𝑥 2 8𝑥
2𝑥 6𝑥 2 −4𝑥
−
−
1 −3𝑥 −8
1 −3𝑥 2
3𝑥 − 2 2𝑥 − 1 = 0
3𝑥 − 2 = 0 2𝑥 − 1 = 0
+1 + 1
+2 + 2
2𝑥 = 1
5𝑥 = 2
2
2
5
5
𝟏
𝟐
𝒙=
𝒙=
𝟓
𝟐
3𝑥 + 8 𝑥 − 1 = 0
3𝑥 + 8 = 0
𝑥−1 =0
−8 − 8
+1 + 1
3𝑥 = −8
𝒙=𝟏
3
3
𝟖
𝒙=−
𝟑
4.4 FACTORING QUADRATICS IN STANDARD FORM
EXAMPLE: Factor then solve the following quadratic
equations.
1. 5𝑥 2 − 17𝑥 + 6 = 0
2. 3𝑥 2 + 20𝑥 − 7 = 0
𝑥 + 7
5𝑥 − 2
= 20𝑥
= −17𝑥
3𝑥 3𝑥 2 21𝑥
𝑥 5𝑥 2 −2𝑥
−
−
1 −1𝑥 −7
3 −15𝑥 6
5𝑥 − 2 𝑥 − 3 = 0
5𝑥 − 2 = 0
𝑥−3 =0
+2 + 2
+3 + 3
5𝑥 = 2
𝒙=𝟑
5
5
𝟐
𝒙=
𝟓
3𝑥 − 1 𝑥 + 7 = 0
3𝑥 − 1 = 0
𝑥+7 =0
+1 + 1
−7 − 7
3𝑥 = 1
𝒙 = −𝟕
3
3
𝟏
𝒙=
𝟑
4.4 FACTORING QUADRATICS IN STANDARD FORM
EXAMPLE: Factor then solve the following quadratic
equations.
1. 2𝑥 2 + 11𝑥 + 12 = 0
2. 3𝑥 2 − 10𝑥 − 8 = 0
3𝑥 + 2
2𝑥 + 3
= −10𝑥
= 11𝑥
𝑥 3𝑥 2 2𝑥
𝑥 2𝑥 2 3𝑥
−
+
12
4 −12𝑥 −8
4 8𝑥
2𝑥 + 3 𝑥 + 4 = 0
2𝑥 + 3 = 0
𝑥+4 =0
−3 − 3
−4 − 4
2𝑥 = −3
𝒙 = −𝟒
2
2
𝟑
𝒙=−
𝟐
3𝑥 + 2 𝑥 − 4 = 0
3𝑥 + 2 = 0
𝑥−4 =0
−2 − 2
+4 + 4
3𝑥 = −2
𝒙=𝟒
3
3
𝟐
𝒙=−
𝟑
4.4 FACTORING QUADRATICS IN STANDARD FORM
EXAMPLE: Factor then solve the following quadratic
equations.
1. 15𝑥 2 − 2𝑥 − 8 = 0
2. 9𝑥 2 − 13𝑥 − 10 = 0
9𝑥 + 5
3𝑥 + 2
= −13𝑥
= −2𝑥
5𝑥 15𝑥 2 10𝑥
𝑥 9𝑥 2 5𝑥
−
−
2 −18𝑥 −10
4 −12𝑥 −8
3𝑥 + 2 5𝑥 − 4 = 0
3𝑥 + 2 = 0 5𝑥 − 4 = 0
−2 − 2
+4 + 4
3𝑥 = −2
5𝑥 = 4
3
3
5
5
𝟐
𝟒
𝒙=−
𝒙=
𝟑
𝟓
9𝑥 + 5 𝑥 − 2 = 0
9𝑥 + 5 = 0
𝑥−2 =0
−5 − 5
+2 + 2
9𝑥 = −5
𝒙=𝟐
9
9
𝒙=
𝟓
−
𝟗
IN CLASS WORK #4:
Solving Quadratics in Factored Form
Previous Assignments:
#1: Graphing Quadratics in Standard Form WS #1
#2: Graphing Quadratics in Vertex Form WS #2
#3: Solving Quadratics in Factored From WS #3
Slide 3
TODAY IN ALGEBRA 2.0…
Warm Up: Zeros in Factored Form
Learning Goal 1: 4.4 You will solve
quadratics in factored form.
Independent Practice
WARM UP: Factor then solve the following quadratic
equations.
1. 𝑥 2 − 16𝑥 + 64 = 0
64
∗
−𝟖 −𝟖
+
−16
𝑥−8 𝑥−8 =0
𝑥−8 =0
+8 + 8
𝒙=𝟖
𝑥−8 =0
+8 + 8
𝒙=𝟖
2. 𝑥 2 − 11𝑥 + 30 = 0
30
∗
−𝟓 −𝟔
+
−11
𝑥−5 𝑥−6 =0
𝑥−5 =0
+5 + 5
𝒙=𝟓
𝑥−6 =0
+6 + 6
𝒙=𝟔
REMEMBER WHY FACTORED FORM IS IMPORTANT…
Below is the graph 𝑦 = 𝑥 2 + 2𝑥 − 8
ZEROS: Where the graph goes
through the x-axis
𝑥 = −4 𝑥 = 2
We can rewrite the equation
using the zeros:
𝑦 = 𝑥 2 + 2𝑥 − 8
𝑦 = (𝑥 + 4)(𝑥 − 2)
This is what you called
FACTORED FORM.
*Notice the signs inside the
parenthesis are opposite…
4.4 FACTORING QUADRATICS IN STANDARD FORM
TRINOMIAL FACTORING RULES:
If
𝑎𝑥 2 + 𝑏𝑥 + 𝑐
then ( +
)( +
If
𝑎𝑥 2 − 𝑏𝑥 + 𝑐
then ( −
)( −
Factored form have
the same signs.
)
If
𝑎𝑥 2 + 𝑏𝑥 − 𝑐
then ( +
)( −
)
)
If
𝑎𝑥 2 − 𝑏𝑥 − 𝑐
then ( +
)( −
)
Factored form have
the different signs.
4.4 FACTORING QUADRATICS IN STANDARD FORM
EXAMPLE: Factor then solve the following quadratic
equations.
1. 6𝑥 2 − 7𝑥 + 2 = 0
2. 3𝑥 2 + 5𝑥 − 8 = 0
3𝑥 + 8
3𝑥 − 2
= 5𝑥
= −7𝑥
𝑥 3𝑥 2 8𝑥
2𝑥 6𝑥 2 −4𝑥
−
−
1 −3𝑥 −8
1 −3𝑥 2
3𝑥 − 2 2𝑥 − 1 = 0
3𝑥 − 2 = 0 2𝑥 − 1 = 0
+1 + 1
+2 + 2
2𝑥 = 1
5𝑥 = 2
2
2
5
5
𝟏
𝟐
𝒙=
𝒙=
𝟓
𝟐
3𝑥 + 8 𝑥 − 1 = 0
3𝑥 + 8 = 0
𝑥−1 =0
−8 − 8
+1 + 1
3𝑥 = −8
𝒙=𝟏
3
3
𝟖
𝒙=−
𝟑
4.4 FACTORING QUADRATICS IN STANDARD FORM
EXAMPLE: Factor then solve the following quadratic
equations.
1. 5𝑥 2 − 17𝑥 + 6 = 0
2. 3𝑥 2 + 20𝑥 − 7 = 0
𝑥 + 7
5𝑥 − 2
= 20𝑥
= −17𝑥
3𝑥 3𝑥 2 21𝑥
𝑥 5𝑥 2 −2𝑥
−
−
1 −1𝑥 −7
3 −15𝑥 6
5𝑥 − 2 𝑥 − 3 = 0
5𝑥 − 2 = 0
𝑥−3 =0
+2 + 2
+3 + 3
5𝑥 = 2
𝒙=𝟑
5
5
𝟐
𝒙=
𝟓
3𝑥 − 1 𝑥 + 7 = 0
3𝑥 − 1 = 0
𝑥+7 =0
+1 + 1
−7 − 7
3𝑥 = 1
𝒙 = −𝟕
3
3
𝟏
𝒙=
𝟑
4.4 FACTORING QUADRATICS IN STANDARD FORM
EXAMPLE: Factor then solve the following quadratic
equations.
1. 2𝑥 2 + 11𝑥 + 12 = 0
2. 3𝑥 2 − 10𝑥 − 8 = 0
3𝑥 + 2
2𝑥 + 3
= −10𝑥
= 11𝑥
𝑥 3𝑥 2 2𝑥
𝑥 2𝑥 2 3𝑥
−
+
12
4 −12𝑥 −8
4 8𝑥
2𝑥 + 3 𝑥 + 4 = 0
2𝑥 + 3 = 0
𝑥+4 =0
−3 − 3
−4 − 4
2𝑥 = −3
𝒙 = −𝟒
2
2
𝟑
𝒙=−
𝟐
3𝑥 + 2 𝑥 − 4 = 0
3𝑥 + 2 = 0
𝑥−4 =0
−2 − 2
+4 + 4
3𝑥 = −2
𝒙=𝟒
3
3
𝟐
𝒙=−
𝟑
4.4 FACTORING QUADRATICS IN STANDARD FORM
EXAMPLE: Factor then solve the following quadratic
equations.
1. 15𝑥 2 − 2𝑥 − 8 = 0
2. 9𝑥 2 − 13𝑥 − 10 = 0
9𝑥 + 5
3𝑥 + 2
= −13𝑥
= −2𝑥
5𝑥 15𝑥 2 10𝑥
𝑥 9𝑥 2 5𝑥
−
−
2 −18𝑥 −10
4 −12𝑥 −8
3𝑥 + 2 5𝑥 − 4 = 0
3𝑥 + 2 = 0 5𝑥 − 4 = 0
−2 − 2
+4 + 4
3𝑥 = −2
5𝑥 = 4
3
3
5
5
𝟐
𝟒
𝒙=−
𝒙=
𝟑
𝟓
9𝑥 + 5 𝑥 − 2 = 0
9𝑥 + 5 = 0
𝑥−2 =0
−5 − 5
+2 + 2
9𝑥 = −5
𝒙=𝟐
9
9
𝒙=
𝟓
−
𝟗
IN CLASS WORK #4:
Solving Quadratics in Factored Form
Previous Assignments:
#1: Graphing Quadratics in Standard Form WS #1
#2: Graphing Quadratics in Vertex Form WS #2
#3: Solving Quadratics in Factored From WS #3
Slide 4
TODAY IN ALGEBRA 2.0…
Warm Up: Zeros in Factored Form
Learning Goal 1: 4.4 You will solve
quadratics in factored form.
Independent Practice
WARM UP: Factor then solve the following quadratic
equations.
1. 𝑥 2 − 16𝑥 + 64 = 0
64
∗
−𝟖 −𝟖
+
−16
𝑥−8 𝑥−8 =0
𝑥−8 =0
+8 + 8
𝒙=𝟖
𝑥−8 =0
+8 + 8
𝒙=𝟖
2. 𝑥 2 − 11𝑥 + 30 = 0
30
∗
−𝟓 −𝟔
+
−11
𝑥−5 𝑥−6 =0
𝑥−5 =0
+5 + 5
𝒙=𝟓
𝑥−6 =0
+6 + 6
𝒙=𝟔
REMEMBER WHY FACTORED FORM IS IMPORTANT…
Below is the graph 𝑦 = 𝑥 2 + 2𝑥 − 8
ZEROS: Where the graph goes
through the x-axis
𝑥 = −4 𝑥 = 2
We can rewrite the equation
using the zeros:
𝑦 = 𝑥 2 + 2𝑥 − 8
𝑦 = (𝑥 + 4)(𝑥 − 2)
This is what you called
FACTORED FORM.
*Notice the signs inside the
parenthesis are opposite…
4.4 FACTORING QUADRATICS IN STANDARD FORM
TRINOMIAL FACTORING RULES:
If
𝑎𝑥 2 + 𝑏𝑥 + 𝑐
then ( +
)( +
If
𝑎𝑥 2 − 𝑏𝑥 + 𝑐
then ( −
)( −
Factored form have
the same signs.
)
If
𝑎𝑥 2 + 𝑏𝑥 − 𝑐
then ( +
)( −
)
)
If
𝑎𝑥 2 − 𝑏𝑥 − 𝑐
then ( +
)( −
)
Factored form have
the different signs.
4.4 FACTORING QUADRATICS IN STANDARD FORM
EXAMPLE: Factor then solve the following quadratic
equations.
1. 6𝑥 2 − 7𝑥 + 2 = 0
2. 3𝑥 2 + 5𝑥 − 8 = 0
3𝑥 + 8
3𝑥 − 2
= 5𝑥
= −7𝑥
𝑥 3𝑥 2 8𝑥
2𝑥 6𝑥 2 −4𝑥
−
−
1 −3𝑥 −8
1 −3𝑥 2
3𝑥 − 2 2𝑥 − 1 = 0
3𝑥 − 2 = 0 2𝑥 − 1 = 0
+1 + 1
+2 + 2
2𝑥 = 1
5𝑥 = 2
2
2
5
5
𝟏
𝟐
𝒙=
𝒙=
𝟓
𝟐
3𝑥 + 8 𝑥 − 1 = 0
3𝑥 + 8 = 0
𝑥−1 =0
−8 − 8
+1 + 1
3𝑥 = −8
𝒙=𝟏
3
3
𝟖
𝒙=−
𝟑
4.4 FACTORING QUADRATICS IN STANDARD FORM
EXAMPLE: Factor then solve the following quadratic
equations.
1. 5𝑥 2 − 17𝑥 + 6 = 0
2. 3𝑥 2 + 20𝑥 − 7 = 0
𝑥 + 7
5𝑥 − 2
= 20𝑥
= −17𝑥
3𝑥 3𝑥 2 21𝑥
𝑥 5𝑥 2 −2𝑥
−
−
1 −1𝑥 −7
3 −15𝑥 6
5𝑥 − 2 𝑥 − 3 = 0
5𝑥 − 2 = 0
𝑥−3 =0
+2 + 2
+3 + 3
5𝑥 = 2
𝒙=𝟑
5
5
𝟐
𝒙=
𝟓
3𝑥 − 1 𝑥 + 7 = 0
3𝑥 − 1 = 0
𝑥+7 =0
+1 + 1
−7 − 7
3𝑥 = 1
𝒙 = −𝟕
3
3
𝟏
𝒙=
𝟑
4.4 FACTORING QUADRATICS IN STANDARD FORM
EXAMPLE: Factor then solve the following quadratic
equations.
1. 2𝑥 2 + 11𝑥 + 12 = 0
2. 3𝑥 2 − 10𝑥 − 8 = 0
3𝑥 + 2
2𝑥 + 3
= −10𝑥
= 11𝑥
𝑥 3𝑥 2 2𝑥
𝑥 2𝑥 2 3𝑥
−
+
12
4 −12𝑥 −8
4 8𝑥
2𝑥 + 3 𝑥 + 4 = 0
2𝑥 + 3 = 0
𝑥+4 =0
−3 − 3
−4 − 4
2𝑥 = −3
𝒙 = −𝟒
2
2
𝟑
𝒙=−
𝟐
3𝑥 + 2 𝑥 − 4 = 0
3𝑥 + 2 = 0
𝑥−4 =0
−2 − 2
+4 + 4
3𝑥 = −2
𝒙=𝟒
3
3
𝟐
𝒙=−
𝟑
4.4 FACTORING QUADRATICS IN STANDARD FORM
EXAMPLE: Factor then solve the following quadratic
equations.
1. 15𝑥 2 − 2𝑥 − 8 = 0
2. 9𝑥 2 − 13𝑥 − 10 = 0
9𝑥 + 5
3𝑥 + 2
= −13𝑥
= −2𝑥
5𝑥 15𝑥 2 10𝑥
𝑥 9𝑥 2 5𝑥
−
−
2 −18𝑥 −10
4 −12𝑥 −8
3𝑥 + 2 5𝑥 − 4 = 0
3𝑥 + 2 = 0 5𝑥 − 4 = 0
−2 − 2
+4 + 4
3𝑥 = −2
5𝑥 = 4
3
3
5
5
𝟐
𝟒
𝒙=−
𝒙=
𝟑
𝟓
9𝑥 + 5 𝑥 − 2 = 0
9𝑥 + 5 = 0
𝑥−2 =0
−5 − 5
+2 + 2
9𝑥 = −5
𝒙=𝟐
9
9
𝒙=
𝟓
−
𝟗
IN CLASS WORK #4:
Solving Quadratics in Factored Form
Previous Assignments:
#1: Graphing Quadratics in Standard Form WS #1
#2: Graphing Quadratics in Vertex Form WS #2
#3: Solving Quadratics in Factored From WS #3
Slide 5
TODAY IN ALGEBRA 2.0…
Warm Up: Zeros in Factored Form
Learning Goal 1: 4.4 You will solve
quadratics in factored form.
Independent Practice
WARM UP: Factor then solve the following quadratic
equations.
1. 𝑥 2 − 16𝑥 + 64 = 0
64
∗
−𝟖 −𝟖
+
−16
𝑥−8 𝑥−8 =0
𝑥−8 =0
+8 + 8
𝒙=𝟖
𝑥−8 =0
+8 + 8
𝒙=𝟖
2. 𝑥 2 − 11𝑥 + 30 = 0
30
∗
−𝟓 −𝟔
+
−11
𝑥−5 𝑥−6 =0
𝑥−5 =0
+5 + 5
𝒙=𝟓
𝑥−6 =0
+6 + 6
𝒙=𝟔
REMEMBER WHY FACTORED FORM IS IMPORTANT…
Below is the graph 𝑦 = 𝑥 2 + 2𝑥 − 8
ZEROS: Where the graph goes
through the x-axis
𝑥 = −4 𝑥 = 2
We can rewrite the equation
using the zeros:
𝑦 = 𝑥 2 + 2𝑥 − 8
𝑦 = (𝑥 + 4)(𝑥 − 2)
This is what you called
FACTORED FORM.
*Notice the signs inside the
parenthesis are opposite…
4.4 FACTORING QUADRATICS IN STANDARD FORM
TRINOMIAL FACTORING RULES:
If
𝑎𝑥 2 + 𝑏𝑥 + 𝑐
then ( +
)( +
If
𝑎𝑥 2 − 𝑏𝑥 + 𝑐
then ( −
)( −
Factored form have
the same signs.
)
If
𝑎𝑥 2 + 𝑏𝑥 − 𝑐
then ( +
)( −
)
)
If
𝑎𝑥 2 − 𝑏𝑥 − 𝑐
then ( +
)( −
)
Factored form have
the different signs.
4.4 FACTORING QUADRATICS IN STANDARD FORM
EXAMPLE: Factor then solve the following quadratic
equations.
1. 6𝑥 2 − 7𝑥 + 2 = 0
2. 3𝑥 2 + 5𝑥 − 8 = 0
3𝑥 + 8
3𝑥 − 2
= 5𝑥
= −7𝑥
𝑥 3𝑥 2 8𝑥
2𝑥 6𝑥 2 −4𝑥
−
−
1 −3𝑥 −8
1 −3𝑥 2
3𝑥 − 2 2𝑥 − 1 = 0
3𝑥 − 2 = 0 2𝑥 − 1 = 0
+1 + 1
+2 + 2
2𝑥 = 1
5𝑥 = 2
2
2
5
5
𝟏
𝟐
𝒙=
𝒙=
𝟓
𝟐
3𝑥 + 8 𝑥 − 1 = 0
3𝑥 + 8 = 0
𝑥−1 =0
−8 − 8
+1 + 1
3𝑥 = −8
𝒙=𝟏
3
3
𝟖
𝒙=−
𝟑
4.4 FACTORING QUADRATICS IN STANDARD FORM
EXAMPLE: Factor then solve the following quadratic
equations.
1. 5𝑥 2 − 17𝑥 + 6 = 0
2. 3𝑥 2 + 20𝑥 − 7 = 0
𝑥 + 7
5𝑥 − 2
= 20𝑥
= −17𝑥
3𝑥 3𝑥 2 21𝑥
𝑥 5𝑥 2 −2𝑥
−
−
1 −1𝑥 −7
3 −15𝑥 6
5𝑥 − 2 𝑥 − 3 = 0
5𝑥 − 2 = 0
𝑥−3 =0
+2 + 2
+3 + 3
5𝑥 = 2
𝒙=𝟑
5
5
𝟐
𝒙=
𝟓
3𝑥 − 1 𝑥 + 7 = 0
3𝑥 − 1 = 0
𝑥+7 =0
+1 + 1
−7 − 7
3𝑥 = 1
𝒙 = −𝟕
3
3
𝟏
𝒙=
𝟑
4.4 FACTORING QUADRATICS IN STANDARD FORM
EXAMPLE: Factor then solve the following quadratic
equations.
1. 2𝑥 2 + 11𝑥 + 12 = 0
2. 3𝑥 2 − 10𝑥 − 8 = 0
3𝑥 + 2
2𝑥 + 3
= −10𝑥
= 11𝑥
𝑥 3𝑥 2 2𝑥
𝑥 2𝑥 2 3𝑥
−
+
12
4 −12𝑥 −8
4 8𝑥
2𝑥 + 3 𝑥 + 4 = 0
2𝑥 + 3 = 0
𝑥+4 =0
−3 − 3
−4 − 4
2𝑥 = −3
𝒙 = −𝟒
2
2
𝟑
𝒙=−
𝟐
3𝑥 + 2 𝑥 − 4 = 0
3𝑥 + 2 = 0
𝑥−4 =0
−2 − 2
+4 + 4
3𝑥 = −2
𝒙=𝟒
3
3
𝟐
𝒙=−
𝟑
4.4 FACTORING QUADRATICS IN STANDARD FORM
EXAMPLE: Factor then solve the following quadratic
equations.
1. 15𝑥 2 − 2𝑥 − 8 = 0
2. 9𝑥 2 − 13𝑥 − 10 = 0
9𝑥 + 5
3𝑥 + 2
= −13𝑥
= −2𝑥
5𝑥 15𝑥 2 10𝑥
𝑥 9𝑥 2 5𝑥
−
−
2 −18𝑥 −10
4 −12𝑥 −8
3𝑥 + 2 5𝑥 − 4 = 0
3𝑥 + 2 = 0 5𝑥 − 4 = 0
−2 − 2
+4 + 4
3𝑥 = −2
5𝑥 = 4
3
3
5
5
𝟐
𝟒
𝒙=−
𝒙=
𝟑
𝟓
9𝑥 + 5 𝑥 − 2 = 0
9𝑥 + 5 = 0
𝑥−2 =0
−5 − 5
+2 + 2
9𝑥 = −5
𝒙=𝟐
9
9
𝒙=
𝟓
−
𝟗
IN CLASS WORK #4:
Solving Quadratics in Factored Form
Previous Assignments:
#1: Graphing Quadratics in Standard Form WS #1
#2: Graphing Quadratics in Vertex Form WS #2
#3: Solving Quadratics in Factored From WS #3
Slide 6
TODAY IN ALGEBRA 2.0…
Warm Up: Zeros in Factored Form
Learning Goal 1: 4.4 You will solve
quadratics in factored form.
Independent Practice
WARM UP: Factor then solve the following quadratic
equations.
1. 𝑥 2 − 16𝑥 + 64 = 0
64
∗
−𝟖 −𝟖
+
−16
𝑥−8 𝑥−8 =0
𝑥−8 =0
+8 + 8
𝒙=𝟖
𝑥−8 =0
+8 + 8
𝒙=𝟖
2. 𝑥 2 − 11𝑥 + 30 = 0
30
∗
−𝟓 −𝟔
+
−11
𝑥−5 𝑥−6 =0
𝑥−5 =0
+5 + 5
𝒙=𝟓
𝑥−6 =0
+6 + 6
𝒙=𝟔
REMEMBER WHY FACTORED FORM IS IMPORTANT…
Below is the graph 𝑦 = 𝑥 2 + 2𝑥 − 8
ZEROS: Where the graph goes
through the x-axis
𝑥 = −4 𝑥 = 2
We can rewrite the equation
using the zeros:
𝑦 = 𝑥 2 + 2𝑥 − 8
𝑦 = (𝑥 + 4)(𝑥 − 2)
This is what you called
FACTORED FORM.
*Notice the signs inside the
parenthesis are opposite…
4.4 FACTORING QUADRATICS IN STANDARD FORM
TRINOMIAL FACTORING RULES:
If
𝑎𝑥 2 + 𝑏𝑥 + 𝑐
then ( +
)( +
If
𝑎𝑥 2 − 𝑏𝑥 + 𝑐
then ( −
)( −
Factored form have
the same signs.
)
If
𝑎𝑥 2 + 𝑏𝑥 − 𝑐
then ( +
)( −
)
)
If
𝑎𝑥 2 − 𝑏𝑥 − 𝑐
then ( +
)( −
)
Factored form have
the different signs.
4.4 FACTORING QUADRATICS IN STANDARD FORM
EXAMPLE: Factor then solve the following quadratic
equations.
1. 6𝑥 2 − 7𝑥 + 2 = 0
2. 3𝑥 2 + 5𝑥 − 8 = 0
3𝑥 + 8
3𝑥 − 2
= 5𝑥
= −7𝑥
𝑥 3𝑥 2 8𝑥
2𝑥 6𝑥 2 −4𝑥
−
−
1 −3𝑥 −8
1 −3𝑥 2
3𝑥 − 2 2𝑥 − 1 = 0
3𝑥 − 2 = 0 2𝑥 − 1 = 0
+1 + 1
+2 + 2
2𝑥 = 1
5𝑥 = 2
2
2
5
5
𝟏
𝟐
𝒙=
𝒙=
𝟓
𝟐
3𝑥 + 8 𝑥 − 1 = 0
3𝑥 + 8 = 0
𝑥−1 =0
−8 − 8
+1 + 1
3𝑥 = −8
𝒙=𝟏
3
3
𝟖
𝒙=−
𝟑
4.4 FACTORING QUADRATICS IN STANDARD FORM
EXAMPLE: Factor then solve the following quadratic
equations.
1. 5𝑥 2 − 17𝑥 + 6 = 0
2. 3𝑥 2 + 20𝑥 − 7 = 0
𝑥 + 7
5𝑥 − 2
= 20𝑥
= −17𝑥
3𝑥 3𝑥 2 21𝑥
𝑥 5𝑥 2 −2𝑥
−
−
1 −1𝑥 −7
3 −15𝑥 6
5𝑥 − 2 𝑥 − 3 = 0
5𝑥 − 2 = 0
𝑥−3 =0
+2 + 2
+3 + 3
5𝑥 = 2
𝒙=𝟑
5
5
𝟐
𝒙=
𝟓
3𝑥 − 1 𝑥 + 7 = 0
3𝑥 − 1 = 0
𝑥+7 =0
+1 + 1
−7 − 7
3𝑥 = 1
𝒙 = −𝟕
3
3
𝟏
𝒙=
𝟑
4.4 FACTORING QUADRATICS IN STANDARD FORM
EXAMPLE: Factor then solve the following quadratic
equations.
1. 2𝑥 2 + 11𝑥 + 12 = 0
2. 3𝑥 2 − 10𝑥 − 8 = 0
3𝑥 + 2
2𝑥 + 3
= −10𝑥
= 11𝑥
𝑥 3𝑥 2 2𝑥
𝑥 2𝑥 2 3𝑥
−
+
12
4 −12𝑥 −8
4 8𝑥
2𝑥 + 3 𝑥 + 4 = 0
2𝑥 + 3 = 0
𝑥+4 =0
−3 − 3
−4 − 4
2𝑥 = −3
𝒙 = −𝟒
2
2
𝟑
𝒙=−
𝟐
3𝑥 + 2 𝑥 − 4 = 0
3𝑥 + 2 = 0
𝑥−4 =0
−2 − 2
+4 + 4
3𝑥 = −2
𝒙=𝟒
3
3
𝟐
𝒙=−
𝟑
4.4 FACTORING QUADRATICS IN STANDARD FORM
EXAMPLE: Factor then solve the following quadratic
equations.
1. 15𝑥 2 − 2𝑥 − 8 = 0
2. 9𝑥 2 − 13𝑥 − 10 = 0
9𝑥 + 5
3𝑥 + 2
= −13𝑥
= −2𝑥
5𝑥 15𝑥 2 10𝑥
𝑥 9𝑥 2 5𝑥
−
−
2 −18𝑥 −10
4 −12𝑥 −8
3𝑥 + 2 5𝑥 − 4 = 0
3𝑥 + 2 = 0 5𝑥 − 4 = 0
−2 − 2
+4 + 4
3𝑥 = −2
5𝑥 = 4
3
3
5
5
𝟐
𝟒
𝒙=−
𝒙=
𝟑
𝟓
9𝑥 + 5 𝑥 − 2 = 0
9𝑥 + 5 = 0
𝑥−2 =0
−5 − 5
+2 + 2
9𝑥 = −5
𝒙=𝟐
9
9
𝒙=
𝟓
−
𝟗
IN CLASS WORK #4:
Solving Quadratics in Factored Form
Previous Assignments:
#1: Graphing Quadratics in Standard Form WS #1
#2: Graphing Quadratics in Vertex Form WS #2
#3: Solving Quadratics in Factored From WS #3
Slide 7
TODAY IN ALGEBRA 2.0…
Warm Up: Zeros in Factored Form
Learning Goal 1: 4.4 You will solve
quadratics in factored form.
Independent Practice
WARM UP: Factor then solve the following quadratic
equations.
1. 𝑥 2 − 16𝑥 + 64 = 0
64
∗
−𝟖 −𝟖
+
−16
𝑥−8 𝑥−8 =0
𝑥−8 =0
+8 + 8
𝒙=𝟖
𝑥−8 =0
+8 + 8
𝒙=𝟖
2. 𝑥 2 − 11𝑥 + 30 = 0
30
∗
−𝟓 −𝟔
+
−11
𝑥−5 𝑥−6 =0
𝑥−5 =0
+5 + 5
𝒙=𝟓
𝑥−6 =0
+6 + 6
𝒙=𝟔
REMEMBER WHY FACTORED FORM IS IMPORTANT…
Below is the graph 𝑦 = 𝑥 2 + 2𝑥 − 8
ZEROS: Where the graph goes
through the x-axis
𝑥 = −4 𝑥 = 2
We can rewrite the equation
using the zeros:
𝑦 = 𝑥 2 + 2𝑥 − 8
𝑦 = (𝑥 + 4)(𝑥 − 2)
This is what you called
FACTORED FORM.
*Notice the signs inside the
parenthesis are opposite…
4.4 FACTORING QUADRATICS IN STANDARD FORM
TRINOMIAL FACTORING RULES:
If
𝑎𝑥 2 + 𝑏𝑥 + 𝑐
then ( +
)( +
If
𝑎𝑥 2 − 𝑏𝑥 + 𝑐
then ( −
)( −
Factored form have
the same signs.
)
If
𝑎𝑥 2 + 𝑏𝑥 − 𝑐
then ( +
)( −
)
)
If
𝑎𝑥 2 − 𝑏𝑥 − 𝑐
then ( +
)( −
)
Factored form have
the different signs.
4.4 FACTORING QUADRATICS IN STANDARD FORM
EXAMPLE: Factor then solve the following quadratic
equations.
1. 6𝑥 2 − 7𝑥 + 2 = 0
2. 3𝑥 2 + 5𝑥 − 8 = 0
3𝑥 + 8
3𝑥 − 2
= 5𝑥
= −7𝑥
𝑥 3𝑥 2 8𝑥
2𝑥 6𝑥 2 −4𝑥
−
−
1 −3𝑥 −8
1 −3𝑥 2
3𝑥 − 2 2𝑥 − 1 = 0
3𝑥 − 2 = 0 2𝑥 − 1 = 0
+1 + 1
+2 + 2
2𝑥 = 1
5𝑥 = 2
2
2
5
5
𝟏
𝟐
𝒙=
𝒙=
𝟓
𝟐
3𝑥 + 8 𝑥 − 1 = 0
3𝑥 + 8 = 0
𝑥−1 =0
−8 − 8
+1 + 1
3𝑥 = −8
𝒙=𝟏
3
3
𝟖
𝒙=−
𝟑
4.4 FACTORING QUADRATICS IN STANDARD FORM
EXAMPLE: Factor then solve the following quadratic
equations.
1. 5𝑥 2 − 17𝑥 + 6 = 0
2. 3𝑥 2 + 20𝑥 − 7 = 0
𝑥 + 7
5𝑥 − 2
= 20𝑥
= −17𝑥
3𝑥 3𝑥 2 21𝑥
𝑥 5𝑥 2 −2𝑥
−
−
1 −1𝑥 −7
3 −15𝑥 6
5𝑥 − 2 𝑥 − 3 = 0
5𝑥 − 2 = 0
𝑥−3 =0
+2 + 2
+3 + 3
5𝑥 = 2
𝒙=𝟑
5
5
𝟐
𝒙=
𝟓
3𝑥 − 1 𝑥 + 7 = 0
3𝑥 − 1 = 0
𝑥+7 =0
+1 + 1
−7 − 7
3𝑥 = 1
𝒙 = −𝟕
3
3
𝟏
𝒙=
𝟑
4.4 FACTORING QUADRATICS IN STANDARD FORM
EXAMPLE: Factor then solve the following quadratic
equations.
1. 2𝑥 2 + 11𝑥 + 12 = 0
2. 3𝑥 2 − 10𝑥 − 8 = 0
3𝑥 + 2
2𝑥 + 3
= −10𝑥
= 11𝑥
𝑥 3𝑥 2 2𝑥
𝑥 2𝑥 2 3𝑥
−
+
12
4 −12𝑥 −8
4 8𝑥
2𝑥 + 3 𝑥 + 4 = 0
2𝑥 + 3 = 0
𝑥+4 =0
−3 − 3
−4 − 4
2𝑥 = −3
𝒙 = −𝟒
2
2
𝟑
𝒙=−
𝟐
3𝑥 + 2 𝑥 − 4 = 0
3𝑥 + 2 = 0
𝑥−4 =0
−2 − 2
+4 + 4
3𝑥 = −2
𝒙=𝟒
3
3
𝟐
𝒙=−
𝟑
4.4 FACTORING QUADRATICS IN STANDARD FORM
EXAMPLE: Factor then solve the following quadratic
equations.
1. 15𝑥 2 − 2𝑥 − 8 = 0
2. 9𝑥 2 − 13𝑥 − 10 = 0
9𝑥 + 5
3𝑥 + 2
= −13𝑥
= −2𝑥
5𝑥 15𝑥 2 10𝑥
𝑥 9𝑥 2 5𝑥
−
−
2 −18𝑥 −10
4 −12𝑥 −8
3𝑥 + 2 5𝑥 − 4 = 0
3𝑥 + 2 = 0 5𝑥 − 4 = 0
−2 − 2
+4 + 4
3𝑥 = −2
5𝑥 = 4
3
3
5
5
𝟐
𝟒
𝒙=−
𝒙=
𝟑
𝟓
9𝑥 + 5 𝑥 − 2 = 0
9𝑥 + 5 = 0
𝑥−2 =0
−5 − 5
+2 + 2
9𝑥 = −5
𝒙=𝟐
9
9
𝒙=
𝟓
−
𝟗
IN CLASS WORK #4:
Solving Quadratics in Factored Form
Previous Assignments:
#1: Graphing Quadratics in Standard Form WS #1
#2: Graphing Quadratics in Vertex Form WS #2
#3: Solving Quadratics in Factored From WS #3
Slide 8
TODAY IN ALGEBRA 2.0…
Warm Up: Zeros in Factored Form
Learning Goal 1: 4.4 You will solve
quadratics in factored form.
Independent Practice
WARM UP: Factor then solve the following quadratic
equations.
1. 𝑥 2 − 16𝑥 + 64 = 0
64
∗
−𝟖 −𝟖
+
−16
𝑥−8 𝑥−8 =0
𝑥−8 =0
+8 + 8
𝒙=𝟖
𝑥−8 =0
+8 + 8
𝒙=𝟖
2. 𝑥 2 − 11𝑥 + 30 = 0
30
∗
−𝟓 −𝟔
+
−11
𝑥−5 𝑥−6 =0
𝑥−5 =0
+5 + 5
𝒙=𝟓
𝑥−6 =0
+6 + 6
𝒙=𝟔
REMEMBER WHY FACTORED FORM IS IMPORTANT…
Below is the graph 𝑦 = 𝑥 2 + 2𝑥 − 8
ZEROS: Where the graph goes
through the x-axis
𝑥 = −4 𝑥 = 2
We can rewrite the equation
using the zeros:
𝑦 = 𝑥 2 + 2𝑥 − 8
𝑦 = (𝑥 + 4)(𝑥 − 2)
This is what you called
FACTORED FORM.
*Notice the signs inside the
parenthesis are opposite…
4.4 FACTORING QUADRATICS IN STANDARD FORM
TRINOMIAL FACTORING RULES:
If
𝑎𝑥 2 + 𝑏𝑥 + 𝑐
then ( +
)( +
If
𝑎𝑥 2 − 𝑏𝑥 + 𝑐
then ( −
)( −
Factored form have
the same signs.
)
If
𝑎𝑥 2 + 𝑏𝑥 − 𝑐
then ( +
)( −
)
)
If
𝑎𝑥 2 − 𝑏𝑥 − 𝑐
then ( +
)( −
)
Factored form have
the different signs.
4.4 FACTORING QUADRATICS IN STANDARD FORM
EXAMPLE: Factor then solve the following quadratic
equations.
1. 6𝑥 2 − 7𝑥 + 2 = 0
2. 3𝑥 2 + 5𝑥 − 8 = 0
3𝑥 + 8
3𝑥 − 2
= 5𝑥
= −7𝑥
𝑥 3𝑥 2 8𝑥
2𝑥 6𝑥 2 −4𝑥
−
−
1 −3𝑥 −8
1 −3𝑥 2
3𝑥 − 2 2𝑥 − 1 = 0
3𝑥 − 2 = 0 2𝑥 − 1 = 0
+1 + 1
+2 + 2
2𝑥 = 1
5𝑥 = 2
2
2
5
5
𝟏
𝟐
𝒙=
𝒙=
𝟓
𝟐
3𝑥 + 8 𝑥 − 1 = 0
3𝑥 + 8 = 0
𝑥−1 =0
−8 − 8
+1 + 1
3𝑥 = −8
𝒙=𝟏
3
3
𝟖
𝒙=−
𝟑
4.4 FACTORING QUADRATICS IN STANDARD FORM
EXAMPLE: Factor then solve the following quadratic
equations.
1. 5𝑥 2 − 17𝑥 + 6 = 0
2. 3𝑥 2 + 20𝑥 − 7 = 0
𝑥 + 7
5𝑥 − 2
= 20𝑥
= −17𝑥
3𝑥 3𝑥 2 21𝑥
𝑥 5𝑥 2 −2𝑥
−
−
1 −1𝑥 −7
3 −15𝑥 6
5𝑥 − 2 𝑥 − 3 = 0
5𝑥 − 2 = 0
𝑥−3 =0
+2 + 2
+3 + 3
5𝑥 = 2
𝒙=𝟑
5
5
𝟐
𝒙=
𝟓
3𝑥 − 1 𝑥 + 7 = 0
3𝑥 − 1 = 0
𝑥+7 =0
+1 + 1
−7 − 7
3𝑥 = 1
𝒙 = −𝟕
3
3
𝟏
𝒙=
𝟑
4.4 FACTORING QUADRATICS IN STANDARD FORM
EXAMPLE: Factor then solve the following quadratic
equations.
1. 2𝑥 2 + 11𝑥 + 12 = 0
2. 3𝑥 2 − 10𝑥 − 8 = 0
3𝑥 + 2
2𝑥 + 3
= −10𝑥
= 11𝑥
𝑥 3𝑥 2 2𝑥
𝑥 2𝑥 2 3𝑥
−
+
12
4 −12𝑥 −8
4 8𝑥
2𝑥 + 3 𝑥 + 4 = 0
2𝑥 + 3 = 0
𝑥+4 =0
−3 − 3
−4 − 4
2𝑥 = −3
𝒙 = −𝟒
2
2
𝟑
𝒙=−
𝟐
3𝑥 + 2 𝑥 − 4 = 0
3𝑥 + 2 = 0
𝑥−4 =0
−2 − 2
+4 + 4
3𝑥 = −2
𝒙=𝟒
3
3
𝟐
𝒙=−
𝟑
4.4 FACTORING QUADRATICS IN STANDARD FORM
EXAMPLE: Factor then solve the following quadratic
equations.
1. 15𝑥 2 − 2𝑥 − 8 = 0
2. 9𝑥 2 − 13𝑥 − 10 = 0
9𝑥 + 5
3𝑥 + 2
= −13𝑥
= −2𝑥
5𝑥 15𝑥 2 10𝑥
𝑥 9𝑥 2 5𝑥
−
−
2 −18𝑥 −10
4 −12𝑥 −8
3𝑥 + 2 5𝑥 − 4 = 0
3𝑥 + 2 = 0 5𝑥 − 4 = 0
−2 − 2
+4 + 4
3𝑥 = −2
5𝑥 = 4
3
3
5
5
𝟐
𝟒
𝒙=−
𝒙=
𝟑
𝟓
9𝑥 + 5 𝑥 − 2 = 0
9𝑥 + 5 = 0
𝑥−2 =0
−5 − 5
+2 + 2
9𝑥 = −5
𝒙=𝟐
9
9
𝒙=
𝟓
−
𝟗
IN CLASS WORK #4:
Solving Quadratics in Factored Form
Previous Assignments:
#1: Graphing Quadratics in Standard Form WS #1
#2: Graphing Quadratics in Vertex Form WS #2
#3: Solving Quadratics in Factored From WS #3
Slide 9
TODAY IN ALGEBRA 2.0…
Warm Up: Zeros in Factored Form
Learning Goal 1: 4.4 You will solve
quadratics in factored form.
Independent Practice
WARM UP: Factor then solve the following quadratic
equations.
1. 𝑥 2 − 16𝑥 + 64 = 0
64
∗
−𝟖 −𝟖
+
−16
𝑥−8 𝑥−8 =0
𝑥−8 =0
+8 + 8
𝒙=𝟖
𝑥−8 =0
+8 + 8
𝒙=𝟖
2. 𝑥 2 − 11𝑥 + 30 = 0
30
∗
−𝟓 −𝟔
+
−11
𝑥−5 𝑥−6 =0
𝑥−5 =0
+5 + 5
𝒙=𝟓
𝑥−6 =0
+6 + 6
𝒙=𝟔
REMEMBER WHY FACTORED FORM IS IMPORTANT…
Below is the graph 𝑦 = 𝑥 2 + 2𝑥 − 8
ZEROS: Where the graph goes
through the x-axis
𝑥 = −4 𝑥 = 2
We can rewrite the equation
using the zeros:
𝑦 = 𝑥 2 + 2𝑥 − 8
𝑦 = (𝑥 + 4)(𝑥 − 2)
This is what you called
FACTORED FORM.
*Notice the signs inside the
parenthesis are opposite…
4.4 FACTORING QUADRATICS IN STANDARD FORM
TRINOMIAL FACTORING RULES:
If
𝑎𝑥 2 + 𝑏𝑥 + 𝑐
then ( +
)( +
If
𝑎𝑥 2 − 𝑏𝑥 + 𝑐
then ( −
)( −
Factored form have
the same signs.
)
If
𝑎𝑥 2 + 𝑏𝑥 − 𝑐
then ( +
)( −
)
)
If
𝑎𝑥 2 − 𝑏𝑥 − 𝑐
then ( +
)( −
)
Factored form have
the different signs.
4.4 FACTORING QUADRATICS IN STANDARD FORM
EXAMPLE: Factor then solve the following quadratic
equations.
1. 6𝑥 2 − 7𝑥 + 2 = 0
2. 3𝑥 2 + 5𝑥 − 8 = 0
3𝑥 + 8
3𝑥 − 2
= 5𝑥
= −7𝑥
𝑥 3𝑥 2 8𝑥
2𝑥 6𝑥 2 −4𝑥
−
−
1 −3𝑥 −8
1 −3𝑥 2
3𝑥 − 2 2𝑥 − 1 = 0
3𝑥 − 2 = 0 2𝑥 − 1 = 0
+1 + 1
+2 + 2
2𝑥 = 1
5𝑥 = 2
2
2
5
5
𝟏
𝟐
𝒙=
𝒙=
𝟓
𝟐
3𝑥 + 8 𝑥 − 1 = 0
3𝑥 + 8 = 0
𝑥−1 =0
−8 − 8
+1 + 1
3𝑥 = −8
𝒙=𝟏
3
3
𝟖
𝒙=−
𝟑
4.4 FACTORING QUADRATICS IN STANDARD FORM
EXAMPLE: Factor then solve the following quadratic
equations.
1. 5𝑥 2 − 17𝑥 + 6 = 0
2. 3𝑥 2 + 20𝑥 − 7 = 0
𝑥 + 7
5𝑥 − 2
= 20𝑥
= −17𝑥
3𝑥 3𝑥 2 21𝑥
𝑥 5𝑥 2 −2𝑥
−
−
1 −1𝑥 −7
3 −15𝑥 6
5𝑥 − 2 𝑥 − 3 = 0
5𝑥 − 2 = 0
𝑥−3 =0
+2 + 2
+3 + 3
5𝑥 = 2
𝒙=𝟑
5
5
𝟐
𝒙=
𝟓
3𝑥 − 1 𝑥 + 7 = 0
3𝑥 − 1 = 0
𝑥+7 =0
+1 + 1
−7 − 7
3𝑥 = 1
𝒙 = −𝟕
3
3
𝟏
𝒙=
𝟑
4.4 FACTORING QUADRATICS IN STANDARD FORM
EXAMPLE: Factor then solve the following quadratic
equations.
1. 2𝑥 2 + 11𝑥 + 12 = 0
2. 3𝑥 2 − 10𝑥 − 8 = 0
3𝑥 + 2
2𝑥 + 3
= −10𝑥
= 11𝑥
𝑥 3𝑥 2 2𝑥
𝑥 2𝑥 2 3𝑥
−
+
12
4 −12𝑥 −8
4 8𝑥
2𝑥 + 3 𝑥 + 4 = 0
2𝑥 + 3 = 0
𝑥+4 =0
−3 − 3
−4 − 4
2𝑥 = −3
𝒙 = −𝟒
2
2
𝟑
𝒙=−
𝟐
3𝑥 + 2 𝑥 − 4 = 0
3𝑥 + 2 = 0
𝑥−4 =0
−2 − 2
+4 + 4
3𝑥 = −2
𝒙=𝟒
3
3
𝟐
𝒙=−
𝟑
4.4 FACTORING QUADRATICS IN STANDARD FORM
EXAMPLE: Factor then solve the following quadratic
equations.
1. 15𝑥 2 − 2𝑥 − 8 = 0
2. 9𝑥 2 − 13𝑥 − 10 = 0
9𝑥 + 5
3𝑥 + 2
= −13𝑥
= −2𝑥
5𝑥 15𝑥 2 10𝑥
𝑥 9𝑥 2 5𝑥
−
−
2 −18𝑥 −10
4 −12𝑥 −8
3𝑥 + 2 5𝑥 − 4 = 0
3𝑥 + 2 = 0 5𝑥 − 4 = 0
−2 − 2
+4 + 4
3𝑥 = −2
5𝑥 = 4
3
3
5
5
𝟐
𝟒
𝒙=−
𝒙=
𝟑
𝟓
9𝑥 + 5 𝑥 − 2 = 0
9𝑥 + 5 = 0
𝑥−2 =0
−5 − 5
+2 + 2
9𝑥 = −5
𝒙=𝟐
9
9
𝒙=
𝟓
−
𝟗
IN CLASS WORK #4:
Solving Quadratics in Factored Form
Previous Assignments:
#1: Graphing Quadratics in Standard Form WS #1
#2: Graphing Quadratics in Vertex Form WS #2
#3: Solving Quadratics in Factored From WS #3
TODAY IN ALGEBRA 2.0…
Warm Up: Zeros in Factored Form
Learning Goal 1: 4.4 You will solve
quadratics in factored form.
Independent Practice
WARM UP: Factor then solve the following quadratic
equations.
1. 𝑥 2 − 16𝑥 + 64 = 0
64
∗
−𝟖 −𝟖
+
−16
𝑥−8 𝑥−8 =0
𝑥−8 =0
+8 + 8
𝒙=𝟖
𝑥−8 =0
+8 + 8
𝒙=𝟖
2. 𝑥 2 − 11𝑥 + 30 = 0
30
∗
−𝟓 −𝟔
+
−11
𝑥−5 𝑥−6 =0
𝑥−5 =0
+5 + 5
𝒙=𝟓
𝑥−6 =0
+6 + 6
𝒙=𝟔
REMEMBER WHY FACTORED FORM IS IMPORTANT…
Below is the graph 𝑦 = 𝑥 2 + 2𝑥 − 8
ZEROS: Where the graph goes
through the x-axis
𝑥 = −4 𝑥 = 2
We can rewrite the equation
using the zeros:
𝑦 = 𝑥 2 + 2𝑥 − 8
𝑦 = (𝑥 + 4)(𝑥 − 2)
This is what you called
FACTORED FORM.
*Notice the signs inside the
parenthesis are opposite…
4.4 FACTORING QUADRATICS IN STANDARD FORM
TRINOMIAL FACTORING RULES:
If
𝑎𝑥 2 + 𝑏𝑥 + 𝑐
then ( +
)( +
If
𝑎𝑥 2 − 𝑏𝑥 + 𝑐
then ( −
)( −
Factored form have
the same signs.
)
If
𝑎𝑥 2 + 𝑏𝑥 − 𝑐
then ( +
)( −
)
)
If
𝑎𝑥 2 − 𝑏𝑥 − 𝑐
then ( +
)( −
)
Factored form have
the different signs.
4.4 FACTORING QUADRATICS IN STANDARD FORM
EXAMPLE: Factor then solve the following quadratic
equations.
1. 6𝑥 2 − 7𝑥 + 2 = 0
2. 3𝑥 2 + 5𝑥 − 8 = 0
3𝑥 + 8
3𝑥 − 2
= 5𝑥
= −7𝑥
𝑥 3𝑥 2 8𝑥
2𝑥 6𝑥 2 −4𝑥
−
−
1 −3𝑥 −8
1 −3𝑥 2
3𝑥 − 2 2𝑥 − 1 = 0
3𝑥 − 2 = 0 2𝑥 − 1 = 0
+1 + 1
+2 + 2
2𝑥 = 1
5𝑥 = 2
2
2
5
5
𝟏
𝟐
𝒙=
𝒙=
𝟓
𝟐
3𝑥 + 8 𝑥 − 1 = 0
3𝑥 + 8 = 0
𝑥−1 =0
−8 − 8
+1 + 1
3𝑥 = −8
𝒙=𝟏
3
3
𝟖
𝒙=−
𝟑
4.4 FACTORING QUADRATICS IN STANDARD FORM
EXAMPLE: Factor then solve the following quadratic
equations.
1. 5𝑥 2 − 17𝑥 + 6 = 0
2. 3𝑥 2 + 20𝑥 − 7 = 0
𝑥 + 7
5𝑥 − 2
= 20𝑥
= −17𝑥
3𝑥 3𝑥 2 21𝑥
𝑥 5𝑥 2 −2𝑥
−
−
1 −1𝑥 −7
3 −15𝑥 6
5𝑥 − 2 𝑥 − 3 = 0
5𝑥 − 2 = 0
𝑥−3 =0
+2 + 2
+3 + 3
5𝑥 = 2
𝒙=𝟑
5
5
𝟐
𝒙=
𝟓
3𝑥 − 1 𝑥 + 7 = 0
3𝑥 − 1 = 0
𝑥+7 =0
+1 + 1
−7 − 7
3𝑥 = 1
𝒙 = −𝟕
3
3
𝟏
𝒙=
𝟑
4.4 FACTORING QUADRATICS IN STANDARD FORM
EXAMPLE: Factor then solve the following quadratic
equations.
1. 2𝑥 2 + 11𝑥 + 12 = 0
2. 3𝑥 2 − 10𝑥 − 8 = 0
3𝑥 + 2
2𝑥 + 3
= −10𝑥
= 11𝑥
𝑥 3𝑥 2 2𝑥
𝑥 2𝑥 2 3𝑥
−
+
12
4 −12𝑥 −8
4 8𝑥
2𝑥 + 3 𝑥 + 4 = 0
2𝑥 + 3 = 0
𝑥+4 =0
−3 − 3
−4 − 4
2𝑥 = −3
𝒙 = −𝟒
2
2
𝟑
𝒙=−
𝟐
3𝑥 + 2 𝑥 − 4 = 0
3𝑥 + 2 = 0
𝑥−4 =0
−2 − 2
+4 + 4
3𝑥 = −2
𝒙=𝟒
3
3
𝟐
𝒙=−
𝟑
4.4 FACTORING QUADRATICS IN STANDARD FORM
EXAMPLE: Factor then solve the following quadratic
equations.
1. 15𝑥 2 − 2𝑥 − 8 = 0
2. 9𝑥 2 − 13𝑥 − 10 = 0
9𝑥 + 5
3𝑥 + 2
= −13𝑥
= −2𝑥
5𝑥 15𝑥 2 10𝑥
𝑥 9𝑥 2 5𝑥
−
−
2 −18𝑥 −10
4 −12𝑥 −8
3𝑥 + 2 5𝑥 − 4 = 0
3𝑥 + 2 = 0 5𝑥 − 4 = 0
−2 − 2
+4 + 4
3𝑥 = −2
5𝑥 = 4
3
3
5
5
𝟐
𝟒
𝒙=−
𝒙=
𝟑
𝟓
9𝑥 + 5 𝑥 − 2 = 0
9𝑥 + 5 = 0
𝑥−2 =0
−5 − 5
+2 + 2
9𝑥 = −5
𝒙=𝟐
9
9
𝒙=
𝟓
−
𝟗
IN CLASS WORK #4:
Solving Quadratics in Factored Form
Previous Assignments:
#1: Graphing Quadratics in Standard Form WS #1
#2: Graphing Quadratics in Vertex Form WS #2
#3: Solving Quadratics in Factored From WS #3
Slide 2
TODAY IN ALGEBRA 2.0…
Warm Up: Zeros in Factored Form
Learning Goal 1: 4.4 You will solve
quadratics in factored form.
Independent Practice
WARM UP: Factor then solve the following quadratic
equations.
1. 𝑥 2 − 16𝑥 + 64 = 0
64
∗
−𝟖 −𝟖
+
−16
𝑥−8 𝑥−8 =0
𝑥−8 =0
+8 + 8
𝒙=𝟖
𝑥−8 =0
+8 + 8
𝒙=𝟖
2. 𝑥 2 − 11𝑥 + 30 = 0
30
∗
−𝟓 −𝟔
+
−11
𝑥−5 𝑥−6 =0
𝑥−5 =0
+5 + 5
𝒙=𝟓
𝑥−6 =0
+6 + 6
𝒙=𝟔
REMEMBER WHY FACTORED FORM IS IMPORTANT…
Below is the graph 𝑦 = 𝑥 2 + 2𝑥 − 8
ZEROS: Where the graph goes
through the x-axis
𝑥 = −4 𝑥 = 2
We can rewrite the equation
using the zeros:
𝑦 = 𝑥 2 + 2𝑥 − 8
𝑦 = (𝑥 + 4)(𝑥 − 2)
This is what you called
FACTORED FORM.
*Notice the signs inside the
parenthesis are opposite…
4.4 FACTORING QUADRATICS IN STANDARD FORM
TRINOMIAL FACTORING RULES:
If
𝑎𝑥 2 + 𝑏𝑥 + 𝑐
then ( +
)( +
If
𝑎𝑥 2 − 𝑏𝑥 + 𝑐
then ( −
)( −
Factored form have
the same signs.
)
If
𝑎𝑥 2 + 𝑏𝑥 − 𝑐
then ( +
)( −
)
)
If
𝑎𝑥 2 − 𝑏𝑥 − 𝑐
then ( +
)( −
)
Factored form have
the different signs.
4.4 FACTORING QUADRATICS IN STANDARD FORM
EXAMPLE: Factor then solve the following quadratic
equations.
1. 6𝑥 2 − 7𝑥 + 2 = 0
2. 3𝑥 2 + 5𝑥 − 8 = 0
3𝑥 + 8
3𝑥 − 2
= 5𝑥
= −7𝑥
𝑥 3𝑥 2 8𝑥
2𝑥 6𝑥 2 −4𝑥
−
−
1 −3𝑥 −8
1 −3𝑥 2
3𝑥 − 2 2𝑥 − 1 = 0
3𝑥 − 2 = 0 2𝑥 − 1 = 0
+1 + 1
+2 + 2
2𝑥 = 1
5𝑥 = 2
2
2
5
5
𝟏
𝟐
𝒙=
𝒙=
𝟓
𝟐
3𝑥 + 8 𝑥 − 1 = 0
3𝑥 + 8 = 0
𝑥−1 =0
−8 − 8
+1 + 1
3𝑥 = −8
𝒙=𝟏
3
3
𝟖
𝒙=−
𝟑
4.4 FACTORING QUADRATICS IN STANDARD FORM
EXAMPLE: Factor then solve the following quadratic
equations.
1. 5𝑥 2 − 17𝑥 + 6 = 0
2. 3𝑥 2 + 20𝑥 − 7 = 0
𝑥 + 7
5𝑥 − 2
= 20𝑥
= −17𝑥
3𝑥 3𝑥 2 21𝑥
𝑥 5𝑥 2 −2𝑥
−
−
1 −1𝑥 −7
3 −15𝑥 6
5𝑥 − 2 𝑥 − 3 = 0
5𝑥 − 2 = 0
𝑥−3 =0
+2 + 2
+3 + 3
5𝑥 = 2
𝒙=𝟑
5
5
𝟐
𝒙=
𝟓
3𝑥 − 1 𝑥 + 7 = 0
3𝑥 − 1 = 0
𝑥+7 =0
+1 + 1
−7 − 7
3𝑥 = 1
𝒙 = −𝟕
3
3
𝟏
𝒙=
𝟑
4.4 FACTORING QUADRATICS IN STANDARD FORM
EXAMPLE: Factor then solve the following quadratic
equations.
1. 2𝑥 2 + 11𝑥 + 12 = 0
2. 3𝑥 2 − 10𝑥 − 8 = 0
3𝑥 + 2
2𝑥 + 3
= −10𝑥
= 11𝑥
𝑥 3𝑥 2 2𝑥
𝑥 2𝑥 2 3𝑥
−
+
12
4 −12𝑥 −8
4 8𝑥
2𝑥 + 3 𝑥 + 4 = 0
2𝑥 + 3 = 0
𝑥+4 =0
−3 − 3
−4 − 4
2𝑥 = −3
𝒙 = −𝟒
2
2
𝟑
𝒙=−
𝟐
3𝑥 + 2 𝑥 − 4 = 0
3𝑥 + 2 = 0
𝑥−4 =0
−2 − 2
+4 + 4
3𝑥 = −2
𝒙=𝟒
3
3
𝟐
𝒙=−
𝟑
4.4 FACTORING QUADRATICS IN STANDARD FORM
EXAMPLE: Factor then solve the following quadratic
equations.
1. 15𝑥 2 − 2𝑥 − 8 = 0
2. 9𝑥 2 − 13𝑥 − 10 = 0
9𝑥 + 5
3𝑥 + 2
= −13𝑥
= −2𝑥
5𝑥 15𝑥 2 10𝑥
𝑥 9𝑥 2 5𝑥
−
−
2 −18𝑥 −10
4 −12𝑥 −8
3𝑥 + 2 5𝑥 − 4 = 0
3𝑥 + 2 = 0 5𝑥 − 4 = 0
−2 − 2
+4 + 4
3𝑥 = −2
5𝑥 = 4
3
3
5
5
𝟐
𝟒
𝒙=−
𝒙=
𝟑
𝟓
9𝑥 + 5 𝑥 − 2 = 0
9𝑥 + 5 = 0
𝑥−2 =0
−5 − 5
+2 + 2
9𝑥 = −5
𝒙=𝟐
9
9
𝒙=
𝟓
−
𝟗
IN CLASS WORK #4:
Solving Quadratics in Factored Form
Previous Assignments:
#1: Graphing Quadratics in Standard Form WS #1
#2: Graphing Quadratics in Vertex Form WS #2
#3: Solving Quadratics in Factored From WS #3
Slide 3
TODAY IN ALGEBRA 2.0…
Warm Up: Zeros in Factored Form
Learning Goal 1: 4.4 You will solve
quadratics in factored form.
Independent Practice
WARM UP: Factor then solve the following quadratic
equations.
1. 𝑥 2 − 16𝑥 + 64 = 0
64
∗
−𝟖 −𝟖
+
−16
𝑥−8 𝑥−8 =0
𝑥−8 =0
+8 + 8
𝒙=𝟖
𝑥−8 =0
+8 + 8
𝒙=𝟖
2. 𝑥 2 − 11𝑥 + 30 = 0
30
∗
−𝟓 −𝟔
+
−11
𝑥−5 𝑥−6 =0
𝑥−5 =0
+5 + 5
𝒙=𝟓
𝑥−6 =0
+6 + 6
𝒙=𝟔
REMEMBER WHY FACTORED FORM IS IMPORTANT…
Below is the graph 𝑦 = 𝑥 2 + 2𝑥 − 8
ZEROS: Where the graph goes
through the x-axis
𝑥 = −4 𝑥 = 2
We can rewrite the equation
using the zeros:
𝑦 = 𝑥 2 + 2𝑥 − 8
𝑦 = (𝑥 + 4)(𝑥 − 2)
This is what you called
FACTORED FORM.
*Notice the signs inside the
parenthesis are opposite…
4.4 FACTORING QUADRATICS IN STANDARD FORM
TRINOMIAL FACTORING RULES:
If
𝑎𝑥 2 + 𝑏𝑥 + 𝑐
then ( +
)( +
If
𝑎𝑥 2 − 𝑏𝑥 + 𝑐
then ( −
)( −
Factored form have
the same signs.
)
If
𝑎𝑥 2 + 𝑏𝑥 − 𝑐
then ( +
)( −
)
)
If
𝑎𝑥 2 − 𝑏𝑥 − 𝑐
then ( +
)( −
)
Factored form have
the different signs.
4.4 FACTORING QUADRATICS IN STANDARD FORM
EXAMPLE: Factor then solve the following quadratic
equations.
1. 6𝑥 2 − 7𝑥 + 2 = 0
2. 3𝑥 2 + 5𝑥 − 8 = 0
3𝑥 + 8
3𝑥 − 2
= 5𝑥
= −7𝑥
𝑥 3𝑥 2 8𝑥
2𝑥 6𝑥 2 −4𝑥
−
−
1 −3𝑥 −8
1 −3𝑥 2
3𝑥 − 2 2𝑥 − 1 = 0
3𝑥 − 2 = 0 2𝑥 − 1 = 0
+1 + 1
+2 + 2
2𝑥 = 1
5𝑥 = 2
2
2
5
5
𝟏
𝟐
𝒙=
𝒙=
𝟓
𝟐
3𝑥 + 8 𝑥 − 1 = 0
3𝑥 + 8 = 0
𝑥−1 =0
−8 − 8
+1 + 1
3𝑥 = −8
𝒙=𝟏
3
3
𝟖
𝒙=−
𝟑
4.4 FACTORING QUADRATICS IN STANDARD FORM
EXAMPLE: Factor then solve the following quadratic
equations.
1. 5𝑥 2 − 17𝑥 + 6 = 0
2. 3𝑥 2 + 20𝑥 − 7 = 0
𝑥 + 7
5𝑥 − 2
= 20𝑥
= −17𝑥
3𝑥 3𝑥 2 21𝑥
𝑥 5𝑥 2 −2𝑥
−
−
1 −1𝑥 −7
3 −15𝑥 6
5𝑥 − 2 𝑥 − 3 = 0
5𝑥 − 2 = 0
𝑥−3 =0
+2 + 2
+3 + 3
5𝑥 = 2
𝒙=𝟑
5
5
𝟐
𝒙=
𝟓
3𝑥 − 1 𝑥 + 7 = 0
3𝑥 − 1 = 0
𝑥+7 =0
+1 + 1
−7 − 7
3𝑥 = 1
𝒙 = −𝟕
3
3
𝟏
𝒙=
𝟑
4.4 FACTORING QUADRATICS IN STANDARD FORM
EXAMPLE: Factor then solve the following quadratic
equations.
1. 2𝑥 2 + 11𝑥 + 12 = 0
2. 3𝑥 2 − 10𝑥 − 8 = 0
3𝑥 + 2
2𝑥 + 3
= −10𝑥
= 11𝑥
𝑥 3𝑥 2 2𝑥
𝑥 2𝑥 2 3𝑥
−
+
12
4 −12𝑥 −8
4 8𝑥
2𝑥 + 3 𝑥 + 4 = 0
2𝑥 + 3 = 0
𝑥+4 =0
−3 − 3
−4 − 4
2𝑥 = −3
𝒙 = −𝟒
2
2
𝟑
𝒙=−
𝟐
3𝑥 + 2 𝑥 − 4 = 0
3𝑥 + 2 = 0
𝑥−4 =0
−2 − 2
+4 + 4
3𝑥 = −2
𝒙=𝟒
3
3
𝟐
𝒙=−
𝟑
4.4 FACTORING QUADRATICS IN STANDARD FORM
EXAMPLE: Factor then solve the following quadratic
equations.
1. 15𝑥 2 − 2𝑥 − 8 = 0
2. 9𝑥 2 − 13𝑥 − 10 = 0
9𝑥 + 5
3𝑥 + 2
= −13𝑥
= −2𝑥
5𝑥 15𝑥 2 10𝑥
𝑥 9𝑥 2 5𝑥
−
−
2 −18𝑥 −10
4 −12𝑥 −8
3𝑥 + 2 5𝑥 − 4 = 0
3𝑥 + 2 = 0 5𝑥 − 4 = 0
−2 − 2
+4 + 4
3𝑥 = −2
5𝑥 = 4
3
3
5
5
𝟐
𝟒
𝒙=−
𝒙=
𝟑
𝟓
9𝑥 + 5 𝑥 − 2 = 0
9𝑥 + 5 = 0
𝑥−2 =0
−5 − 5
+2 + 2
9𝑥 = −5
𝒙=𝟐
9
9
𝒙=
𝟓
−
𝟗
IN CLASS WORK #4:
Solving Quadratics in Factored Form
Previous Assignments:
#1: Graphing Quadratics in Standard Form WS #1
#2: Graphing Quadratics in Vertex Form WS #2
#3: Solving Quadratics in Factored From WS #3
Slide 4
TODAY IN ALGEBRA 2.0…
Warm Up: Zeros in Factored Form
Learning Goal 1: 4.4 You will solve
quadratics in factored form.
Independent Practice
WARM UP: Factor then solve the following quadratic
equations.
1. 𝑥 2 − 16𝑥 + 64 = 0
64
∗
−𝟖 −𝟖
+
−16
𝑥−8 𝑥−8 =0
𝑥−8 =0
+8 + 8
𝒙=𝟖
𝑥−8 =0
+8 + 8
𝒙=𝟖
2. 𝑥 2 − 11𝑥 + 30 = 0
30
∗
−𝟓 −𝟔
+
−11
𝑥−5 𝑥−6 =0
𝑥−5 =0
+5 + 5
𝒙=𝟓
𝑥−6 =0
+6 + 6
𝒙=𝟔
REMEMBER WHY FACTORED FORM IS IMPORTANT…
Below is the graph 𝑦 = 𝑥 2 + 2𝑥 − 8
ZEROS: Where the graph goes
through the x-axis
𝑥 = −4 𝑥 = 2
We can rewrite the equation
using the zeros:
𝑦 = 𝑥 2 + 2𝑥 − 8
𝑦 = (𝑥 + 4)(𝑥 − 2)
This is what you called
FACTORED FORM.
*Notice the signs inside the
parenthesis are opposite…
4.4 FACTORING QUADRATICS IN STANDARD FORM
TRINOMIAL FACTORING RULES:
If
𝑎𝑥 2 + 𝑏𝑥 + 𝑐
then ( +
)( +
If
𝑎𝑥 2 − 𝑏𝑥 + 𝑐
then ( −
)( −
Factored form have
the same signs.
)
If
𝑎𝑥 2 + 𝑏𝑥 − 𝑐
then ( +
)( −
)
)
If
𝑎𝑥 2 − 𝑏𝑥 − 𝑐
then ( +
)( −
)
Factored form have
the different signs.
4.4 FACTORING QUADRATICS IN STANDARD FORM
EXAMPLE: Factor then solve the following quadratic
equations.
1. 6𝑥 2 − 7𝑥 + 2 = 0
2. 3𝑥 2 + 5𝑥 − 8 = 0
3𝑥 + 8
3𝑥 − 2
= 5𝑥
= −7𝑥
𝑥 3𝑥 2 8𝑥
2𝑥 6𝑥 2 −4𝑥
−
−
1 −3𝑥 −8
1 −3𝑥 2
3𝑥 − 2 2𝑥 − 1 = 0
3𝑥 − 2 = 0 2𝑥 − 1 = 0
+1 + 1
+2 + 2
2𝑥 = 1
5𝑥 = 2
2
2
5
5
𝟏
𝟐
𝒙=
𝒙=
𝟓
𝟐
3𝑥 + 8 𝑥 − 1 = 0
3𝑥 + 8 = 0
𝑥−1 =0
−8 − 8
+1 + 1
3𝑥 = −8
𝒙=𝟏
3
3
𝟖
𝒙=−
𝟑
4.4 FACTORING QUADRATICS IN STANDARD FORM
EXAMPLE: Factor then solve the following quadratic
equations.
1. 5𝑥 2 − 17𝑥 + 6 = 0
2. 3𝑥 2 + 20𝑥 − 7 = 0
𝑥 + 7
5𝑥 − 2
= 20𝑥
= −17𝑥
3𝑥 3𝑥 2 21𝑥
𝑥 5𝑥 2 −2𝑥
−
−
1 −1𝑥 −7
3 −15𝑥 6
5𝑥 − 2 𝑥 − 3 = 0
5𝑥 − 2 = 0
𝑥−3 =0
+2 + 2
+3 + 3
5𝑥 = 2
𝒙=𝟑
5
5
𝟐
𝒙=
𝟓
3𝑥 − 1 𝑥 + 7 = 0
3𝑥 − 1 = 0
𝑥+7 =0
+1 + 1
−7 − 7
3𝑥 = 1
𝒙 = −𝟕
3
3
𝟏
𝒙=
𝟑
4.4 FACTORING QUADRATICS IN STANDARD FORM
EXAMPLE: Factor then solve the following quadratic
equations.
1. 2𝑥 2 + 11𝑥 + 12 = 0
2. 3𝑥 2 − 10𝑥 − 8 = 0
3𝑥 + 2
2𝑥 + 3
= −10𝑥
= 11𝑥
𝑥 3𝑥 2 2𝑥
𝑥 2𝑥 2 3𝑥
−
+
12
4 −12𝑥 −8
4 8𝑥
2𝑥 + 3 𝑥 + 4 = 0
2𝑥 + 3 = 0
𝑥+4 =0
−3 − 3
−4 − 4
2𝑥 = −3
𝒙 = −𝟒
2
2
𝟑
𝒙=−
𝟐
3𝑥 + 2 𝑥 − 4 = 0
3𝑥 + 2 = 0
𝑥−4 =0
−2 − 2
+4 + 4
3𝑥 = −2
𝒙=𝟒
3
3
𝟐
𝒙=−
𝟑
4.4 FACTORING QUADRATICS IN STANDARD FORM
EXAMPLE: Factor then solve the following quadratic
equations.
1. 15𝑥 2 − 2𝑥 − 8 = 0
2. 9𝑥 2 − 13𝑥 − 10 = 0
9𝑥 + 5
3𝑥 + 2
= −13𝑥
= −2𝑥
5𝑥 15𝑥 2 10𝑥
𝑥 9𝑥 2 5𝑥
−
−
2 −18𝑥 −10
4 −12𝑥 −8
3𝑥 + 2 5𝑥 − 4 = 0
3𝑥 + 2 = 0 5𝑥 − 4 = 0
−2 − 2
+4 + 4
3𝑥 = −2
5𝑥 = 4
3
3
5
5
𝟐
𝟒
𝒙=−
𝒙=
𝟑
𝟓
9𝑥 + 5 𝑥 − 2 = 0
9𝑥 + 5 = 0
𝑥−2 =0
−5 − 5
+2 + 2
9𝑥 = −5
𝒙=𝟐
9
9
𝒙=
𝟓
−
𝟗
IN CLASS WORK #4:
Solving Quadratics in Factored Form
Previous Assignments:
#1: Graphing Quadratics in Standard Form WS #1
#2: Graphing Quadratics in Vertex Form WS #2
#3: Solving Quadratics in Factored From WS #3
Slide 5
TODAY IN ALGEBRA 2.0…
Warm Up: Zeros in Factored Form
Learning Goal 1: 4.4 You will solve
quadratics in factored form.
Independent Practice
WARM UP: Factor then solve the following quadratic
equations.
1. 𝑥 2 − 16𝑥 + 64 = 0
64
∗
−𝟖 −𝟖
+
−16
𝑥−8 𝑥−8 =0
𝑥−8 =0
+8 + 8
𝒙=𝟖
𝑥−8 =0
+8 + 8
𝒙=𝟖
2. 𝑥 2 − 11𝑥 + 30 = 0
30
∗
−𝟓 −𝟔
+
−11
𝑥−5 𝑥−6 =0
𝑥−5 =0
+5 + 5
𝒙=𝟓
𝑥−6 =0
+6 + 6
𝒙=𝟔
REMEMBER WHY FACTORED FORM IS IMPORTANT…
Below is the graph 𝑦 = 𝑥 2 + 2𝑥 − 8
ZEROS: Where the graph goes
through the x-axis
𝑥 = −4 𝑥 = 2
We can rewrite the equation
using the zeros:
𝑦 = 𝑥 2 + 2𝑥 − 8
𝑦 = (𝑥 + 4)(𝑥 − 2)
This is what you called
FACTORED FORM.
*Notice the signs inside the
parenthesis are opposite…
4.4 FACTORING QUADRATICS IN STANDARD FORM
TRINOMIAL FACTORING RULES:
If
𝑎𝑥 2 + 𝑏𝑥 + 𝑐
then ( +
)( +
If
𝑎𝑥 2 − 𝑏𝑥 + 𝑐
then ( −
)( −
Factored form have
the same signs.
)
If
𝑎𝑥 2 + 𝑏𝑥 − 𝑐
then ( +
)( −
)
)
If
𝑎𝑥 2 − 𝑏𝑥 − 𝑐
then ( +
)( −
)
Factored form have
the different signs.
4.4 FACTORING QUADRATICS IN STANDARD FORM
EXAMPLE: Factor then solve the following quadratic
equations.
1. 6𝑥 2 − 7𝑥 + 2 = 0
2. 3𝑥 2 + 5𝑥 − 8 = 0
3𝑥 + 8
3𝑥 − 2
= 5𝑥
= −7𝑥
𝑥 3𝑥 2 8𝑥
2𝑥 6𝑥 2 −4𝑥
−
−
1 −3𝑥 −8
1 −3𝑥 2
3𝑥 − 2 2𝑥 − 1 = 0
3𝑥 − 2 = 0 2𝑥 − 1 = 0
+1 + 1
+2 + 2
2𝑥 = 1
5𝑥 = 2
2
2
5
5
𝟏
𝟐
𝒙=
𝒙=
𝟓
𝟐
3𝑥 + 8 𝑥 − 1 = 0
3𝑥 + 8 = 0
𝑥−1 =0
−8 − 8
+1 + 1
3𝑥 = −8
𝒙=𝟏
3
3
𝟖
𝒙=−
𝟑
4.4 FACTORING QUADRATICS IN STANDARD FORM
EXAMPLE: Factor then solve the following quadratic
equations.
1. 5𝑥 2 − 17𝑥 + 6 = 0
2. 3𝑥 2 + 20𝑥 − 7 = 0
𝑥 + 7
5𝑥 − 2
= 20𝑥
= −17𝑥
3𝑥 3𝑥 2 21𝑥
𝑥 5𝑥 2 −2𝑥
−
−
1 −1𝑥 −7
3 −15𝑥 6
5𝑥 − 2 𝑥 − 3 = 0
5𝑥 − 2 = 0
𝑥−3 =0
+2 + 2
+3 + 3
5𝑥 = 2
𝒙=𝟑
5
5
𝟐
𝒙=
𝟓
3𝑥 − 1 𝑥 + 7 = 0
3𝑥 − 1 = 0
𝑥+7 =0
+1 + 1
−7 − 7
3𝑥 = 1
𝒙 = −𝟕
3
3
𝟏
𝒙=
𝟑
4.4 FACTORING QUADRATICS IN STANDARD FORM
EXAMPLE: Factor then solve the following quadratic
equations.
1. 2𝑥 2 + 11𝑥 + 12 = 0
2. 3𝑥 2 − 10𝑥 − 8 = 0
3𝑥 + 2
2𝑥 + 3
= −10𝑥
= 11𝑥
𝑥 3𝑥 2 2𝑥
𝑥 2𝑥 2 3𝑥
−
+
12
4 −12𝑥 −8
4 8𝑥
2𝑥 + 3 𝑥 + 4 = 0
2𝑥 + 3 = 0
𝑥+4 =0
−3 − 3
−4 − 4
2𝑥 = −3
𝒙 = −𝟒
2
2
𝟑
𝒙=−
𝟐
3𝑥 + 2 𝑥 − 4 = 0
3𝑥 + 2 = 0
𝑥−4 =0
−2 − 2
+4 + 4
3𝑥 = −2
𝒙=𝟒
3
3
𝟐
𝒙=−
𝟑
4.4 FACTORING QUADRATICS IN STANDARD FORM
EXAMPLE: Factor then solve the following quadratic
equations.
1. 15𝑥 2 − 2𝑥 − 8 = 0
2. 9𝑥 2 − 13𝑥 − 10 = 0
9𝑥 + 5
3𝑥 + 2
= −13𝑥
= −2𝑥
5𝑥 15𝑥 2 10𝑥
𝑥 9𝑥 2 5𝑥
−
−
2 −18𝑥 −10
4 −12𝑥 −8
3𝑥 + 2 5𝑥 − 4 = 0
3𝑥 + 2 = 0 5𝑥 − 4 = 0
−2 − 2
+4 + 4
3𝑥 = −2
5𝑥 = 4
3
3
5
5
𝟐
𝟒
𝒙=−
𝒙=
𝟑
𝟓
9𝑥 + 5 𝑥 − 2 = 0
9𝑥 + 5 = 0
𝑥−2 =0
−5 − 5
+2 + 2
9𝑥 = −5
𝒙=𝟐
9
9
𝒙=
𝟓
−
𝟗
IN CLASS WORK #4:
Solving Quadratics in Factored Form
Previous Assignments:
#1: Graphing Quadratics in Standard Form WS #1
#2: Graphing Quadratics in Vertex Form WS #2
#3: Solving Quadratics in Factored From WS #3
Slide 6
TODAY IN ALGEBRA 2.0…
Warm Up: Zeros in Factored Form
Learning Goal 1: 4.4 You will solve
quadratics in factored form.
Independent Practice
WARM UP: Factor then solve the following quadratic
equations.
1. 𝑥 2 − 16𝑥 + 64 = 0
64
∗
−𝟖 −𝟖
+
−16
𝑥−8 𝑥−8 =0
𝑥−8 =0
+8 + 8
𝒙=𝟖
𝑥−8 =0
+8 + 8
𝒙=𝟖
2. 𝑥 2 − 11𝑥 + 30 = 0
30
∗
−𝟓 −𝟔
+
−11
𝑥−5 𝑥−6 =0
𝑥−5 =0
+5 + 5
𝒙=𝟓
𝑥−6 =0
+6 + 6
𝒙=𝟔
REMEMBER WHY FACTORED FORM IS IMPORTANT…
Below is the graph 𝑦 = 𝑥 2 + 2𝑥 − 8
ZEROS: Where the graph goes
through the x-axis
𝑥 = −4 𝑥 = 2
We can rewrite the equation
using the zeros:
𝑦 = 𝑥 2 + 2𝑥 − 8
𝑦 = (𝑥 + 4)(𝑥 − 2)
This is what you called
FACTORED FORM.
*Notice the signs inside the
parenthesis are opposite…
4.4 FACTORING QUADRATICS IN STANDARD FORM
TRINOMIAL FACTORING RULES:
If
𝑎𝑥 2 + 𝑏𝑥 + 𝑐
then ( +
)( +
If
𝑎𝑥 2 − 𝑏𝑥 + 𝑐
then ( −
)( −
Factored form have
the same signs.
)
If
𝑎𝑥 2 + 𝑏𝑥 − 𝑐
then ( +
)( −
)
)
If
𝑎𝑥 2 − 𝑏𝑥 − 𝑐
then ( +
)( −
)
Factored form have
the different signs.
4.4 FACTORING QUADRATICS IN STANDARD FORM
EXAMPLE: Factor then solve the following quadratic
equations.
1. 6𝑥 2 − 7𝑥 + 2 = 0
2. 3𝑥 2 + 5𝑥 − 8 = 0
3𝑥 + 8
3𝑥 − 2
= 5𝑥
= −7𝑥
𝑥 3𝑥 2 8𝑥
2𝑥 6𝑥 2 −4𝑥
−
−
1 −3𝑥 −8
1 −3𝑥 2
3𝑥 − 2 2𝑥 − 1 = 0
3𝑥 − 2 = 0 2𝑥 − 1 = 0
+1 + 1
+2 + 2
2𝑥 = 1
5𝑥 = 2
2
2
5
5
𝟏
𝟐
𝒙=
𝒙=
𝟓
𝟐
3𝑥 + 8 𝑥 − 1 = 0
3𝑥 + 8 = 0
𝑥−1 =0
−8 − 8
+1 + 1
3𝑥 = −8
𝒙=𝟏
3
3
𝟖
𝒙=−
𝟑
4.4 FACTORING QUADRATICS IN STANDARD FORM
EXAMPLE: Factor then solve the following quadratic
equations.
1. 5𝑥 2 − 17𝑥 + 6 = 0
2. 3𝑥 2 + 20𝑥 − 7 = 0
𝑥 + 7
5𝑥 − 2
= 20𝑥
= −17𝑥
3𝑥 3𝑥 2 21𝑥
𝑥 5𝑥 2 −2𝑥
−
−
1 −1𝑥 −7
3 −15𝑥 6
5𝑥 − 2 𝑥 − 3 = 0
5𝑥 − 2 = 0
𝑥−3 =0
+2 + 2
+3 + 3
5𝑥 = 2
𝒙=𝟑
5
5
𝟐
𝒙=
𝟓
3𝑥 − 1 𝑥 + 7 = 0
3𝑥 − 1 = 0
𝑥+7 =0
+1 + 1
−7 − 7
3𝑥 = 1
𝒙 = −𝟕
3
3
𝟏
𝒙=
𝟑
4.4 FACTORING QUADRATICS IN STANDARD FORM
EXAMPLE: Factor then solve the following quadratic
equations.
1. 2𝑥 2 + 11𝑥 + 12 = 0
2. 3𝑥 2 − 10𝑥 − 8 = 0
3𝑥 + 2
2𝑥 + 3
= −10𝑥
= 11𝑥
𝑥 3𝑥 2 2𝑥
𝑥 2𝑥 2 3𝑥
−
+
12
4 −12𝑥 −8
4 8𝑥
2𝑥 + 3 𝑥 + 4 = 0
2𝑥 + 3 = 0
𝑥+4 =0
−3 − 3
−4 − 4
2𝑥 = −3
𝒙 = −𝟒
2
2
𝟑
𝒙=−
𝟐
3𝑥 + 2 𝑥 − 4 = 0
3𝑥 + 2 = 0
𝑥−4 =0
−2 − 2
+4 + 4
3𝑥 = −2
𝒙=𝟒
3
3
𝟐
𝒙=−
𝟑
4.4 FACTORING QUADRATICS IN STANDARD FORM
EXAMPLE: Factor then solve the following quadratic
equations.
1. 15𝑥 2 − 2𝑥 − 8 = 0
2. 9𝑥 2 − 13𝑥 − 10 = 0
9𝑥 + 5
3𝑥 + 2
= −13𝑥
= −2𝑥
5𝑥 15𝑥 2 10𝑥
𝑥 9𝑥 2 5𝑥
−
−
2 −18𝑥 −10
4 −12𝑥 −8
3𝑥 + 2 5𝑥 − 4 = 0
3𝑥 + 2 = 0 5𝑥 − 4 = 0
−2 − 2
+4 + 4
3𝑥 = −2
5𝑥 = 4
3
3
5
5
𝟐
𝟒
𝒙=−
𝒙=
𝟑
𝟓
9𝑥 + 5 𝑥 − 2 = 0
9𝑥 + 5 = 0
𝑥−2 =0
−5 − 5
+2 + 2
9𝑥 = −5
𝒙=𝟐
9
9
𝒙=
𝟓
−
𝟗
IN CLASS WORK #4:
Solving Quadratics in Factored Form
Previous Assignments:
#1: Graphing Quadratics in Standard Form WS #1
#2: Graphing Quadratics in Vertex Form WS #2
#3: Solving Quadratics in Factored From WS #3
Slide 7
TODAY IN ALGEBRA 2.0…
Warm Up: Zeros in Factored Form
Learning Goal 1: 4.4 You will solve
quadratics in factored form.
Independent Practice
WARM UP: Factor then solve the following quadratic
equations.
1. 𝑥 2 − 16𝑥 + 64 = 0
64
∗
−𝟖 −𝟖
+
−16
𝑥−8 𝑥−8 =0
𝑥−8 =0
+8 + 8
𝒙=𝟖
𝑥−8 =0
+8 + 8
𝒙=𝟖
2. 𝑥 2 − 11𝑥 + 30 = 0
30
∗
−𝟓 −𝟔
+
−11
𝑥−5 𝑥−6 =0
𝑥−5 =0
+5 + 5
𝒙=𝟓
𝑥−6 =0
+6 + 6
𝒙=𝟔
REMEMBER WHY FACTORED FORM IS IMPORTANT…
Below is the graph 𝑦 = 𝑥 2 + 2𝑥 − 8
ZEROS: Where the graph goes
through the x-axis
𝑥 = −4 𝑥 = 2
We can rewrite the equation
using the zeros:
𝑦 = 𝑥 2 + 2𝑥 − 8
𝑦 = (𝑥 + 4)(𝑥 − 2)
This is what you called
FACTORED FORM.
*Notice the signs inside the
parenthesis are opposite…
4.4 FACTORING QUADRATICS IN STANDARD FORM
TRINOMIAL FACTORING RULES:
If
𝑎𝑥 2 + 𝑏𝑥 + 𝑐
then ( +
)( +
If
𝑎𝑥 2 − 𝑏𝑥 + 𝑐
then ( −
)( −
Factored form have
the same signs.
)
If
𝑎𝑥 2 + 𝑏𝑥 − 𝑐
then ( +
)( −
)
)
If
𝑎𝑥 2 − 𝑏𝑥 − 𝑐
then ( +
)( −
)
Factored form have
the different signs.
4.4 FACTORING QUADRATICS IN STANDARD FORM
EXAMPLE: Factor then solve the following quadratic
equations.
1. 6𝑥 2 − 7𝑥 + 2 = 0
2. 3𝑥 2 + 5𝑥 − 8 = 0
3𝑥 + 8
3𝑥 − 2
= 5𝑥
= −7𝑥
𝑥 3𝑥 2 8𝑥
2𝑥 6𝑥 2 −4𝑥
−
−
1 −3𝑥 −8
1 −3𝑥 2
3𝑥 − 2 2𝑥 − 1 = 0
3𝑥 − 2 = 0 2𝑥 − 1 = 0
+1 + 1
+2 + 2
2𝑥 = 1
5𝑥 = 2
2
2
5
5
𝟏
𝟐
𝒙=
𝒙=
𝟓
𝟐
3𝑥 + 8 𝑥 − 1 = 0
3𝑥 + 8 = 0
𝑥−1 =0
−8 − 8
+1 + 1
3𝑥 = −8
𝒙=𝟏
3
3
𝟖
𝒙=−
𝟑
4.4 FACTORING QUADRATICS IN STANDARD FORM
EXAMPLE: Factor then solve the following quadratic
equations.
1. 5𝑥 2 − 17𝑥 + 6 = 0
2. 3𝑥 2 + 20𝑥 − 7 = 0
𝑥 + 7
5𝑥 − 2
= 20𝑥
= −17𝑥
3𝑥 3𝑥 2 21𝑥
𝑥 5𝑥 2 −2𝑥
−
−
1 −1𝑥 −7
3 −15𝑥 6
5𝑥 − 2 𝑥 − 3 = 0
5𝑥 − 2 = 0
𝑥−3 =0
+2 + 2
+3 + 3
5𝑥 = 2
𝒙=𝟑
5
5
𝟐
𝒙=
𝟓
3𝑥 − 1 𝑥 + 7 = 0
3𝑥 − 1 = 0
𝑥+7 =0
+1 + 1
−7 − 7
3𝑥 = 1
𝒙 = −𝟕
3
3
𝟏
𝒙=
𝟑
4.4 FACTORING QUADRATICS IN STANDARD FORM
EXAMPLE: Factor then solve the following quadratic
equations.
1. 2𝑥 2 + 11𝑥 + 12 = 0
2. 3𝑥 2 − 10𝑥 − 8 = 0
3𝑥 + 2
2𝑥 + 3
= −10𝑥
= 11𝑥
𝑥 3𝑥 2 2𝑥
𝑥 2𝑥 2 3𝑥
−
+
12
4 −12𝑥 −8
4 8𝑥
2𝑥 + 3 𝑥 + 4 = 0
2𝑥 + 3 = 0
𝑥+4 =0
−3 − 3
−4 − 4
2𝑥 = −3
𝒙 = −𝟒
2
2
𝟑
𝒙=−
𝟐
3𝑥 + 2 𝑥 − 4 = 0
3𝑥 + 2 = 0
𝑥−4 =0
−2 − 2
+4 + 4
3𝑥 = −2
𝒙=𝟒
3
3
𝟐
𝒙=−
𝟑
4.4 FACTORING QUADRATICS IN STANDARD FORM
EXAMPLE: Factor then solve the following quadratic
equations.
1. 15𝑥 2 − 2𝑥 − 8 = 0
2. 9𝑥 2 − 13𝑥 − 10 = 0
9𝑥 + 5
3𝑥 + 2
= −13𝑥
= −2𝑥
5𝑥 15𝑥 2 10𝑥
𝑥 9𝑥 2 5𝑥
−
−
2 −18𝑥 −10
4 −12𝑥 −8
3𝑥 + 2 5𝑥 − 4 = 0
3𝑥 + 2 = 0 5𝑥 − 4 = 0
−2 − 2
+4 + 4
3𝑥 = −2
5𝑥 = 4
3
3
5
5
𝟐
𝟒
𝒙=−
𝒙=
𝟑
𝟓
9𝑥 + 5 𝑥 − 2 = 0
9𝑥 + 5 = 0
𝑥−2 =0
−5 − 5
+2 + 2
9𝑥 = −5
𝒙=𝟐
9
9
𝒙=
𝟓
−
𝟗
IN CLASS WORK #4:
Solving Quadratics in Factored Form
Previous Assignments:
#1: Graphing Quadratics in Standard Form WS #1
#2: Graphing Quadratics in Vertex Form WS #2
#3: Solving Quadratics in Factored From WS #3
Slide 8
TODAY IN ALGEBRA 2.0…
Warm Up: Zeros in Factored Form
Learning Goal 1: 4.4 You will solve
quadratics in factored form.
Independent Practice
WARM UP: Factor then solve the following quadratic
equations.
1. 𝑥 2 − 16𝑥 + 64 = 0
64
∗
−𝟖 −𝟖
+
−16
𝑥−8 𝑥−8 =0
𝑥−8 =0
+8 + 8
𝒙=𝟖
𝑥−8 =0
+8 + 8
𝒙=𝟖
2. 𝑥 2 − 11𝑥 + 30 = 0
30
∗
−𝟓 −𝟔
+
−11
𝑥−5 𝑥−6 =0
𝑥−5 =0
+5 + 5
𝒙=𝟓
𝑥−6 =0
+6 + 6
𝒙=𝟔
REMEMBER WHY FACTORED FORM IS IMPORTANT…
Below is the graph 𝑦 = 𝑥 2 + 2𝑥 − 8
ZEROS: Where the graph goes
through the x-axis
𝑥 = −4 𝑥 = 2
We can rewrite the equation
using the zeros:
𝑦 = 𝑥 2 + 2𝑥 − 8
𝑦 = (𝑥 + 4)(𝑥 − 2)
This is what you called
FACTORED FORM.
*Notice the signs inside the
parenthesis are opposite…
4.4 FACTORING QUADRATICS IN STANDARD FORM
TRINOMIAL FACTORING RULES:
If
𝑎𝑥 2 + 𝑏𝑥 + 𝑐
then ( +
)( +
If
𝑎𝑥 2 − 𝑏𝑥 + 𝑐
then ( −
)( −
Factored form have
the same signs.
)
If
𝑎𝑥 2 + 𝑏𝑥 − 𝑐
then ( +
)( −
)
)
If
𝑎𝑥 2 − 𝑏𝑥 − 𝑐
then ( +
)( −
)
Factored form have
the different signs.
4.4 FACTORING QUADRATICS IN STANDARD FORM
EXAMPLE: Factor then solve the following quadratic
equations.
1. 6𝑥 2 − 7𝑥 + 2 = 0
2. 3𝑥 2 + 5𝑥 − 8 = 0
3𝑥 + 8
3𝑥 − 2
= 5𝑥
= −7𝑥
𝑥 3𝑥 2 8𝑥
2𝑥 6𝑥 2 −4𝑥
−
−
1 −3𝑥 −8
1 −3𝑥 2
3𝑥 − 2 2𝑥 − 1 = 0
3𝑥 − 2 = 0 2𝑥 − 1 = 0
+1 + 1
+2 + 2
2𝑥 = 1
5𝑥 = 2
2
2
5
5
𝟏
𝟐
𝒙=
𝒙=
𝟓
𝟐
3𝑥 + 8 𝑥 − 1 = 0
3𝑥 + 8 = 0
𝑥−1 =0
−8 − 8
+1 + 1
3𝑥 = −8
𝒙=𝟏
3
3
𝟖
𝒙=−
𝟑
4.4 FACTORING QUADRATICS IN STANDARD FORM
EXAMPLE: Factor then solve the following quadratic
equations.
1. 5𝑥 2 − 17𝑥 + 6 = 0
2. 3𝑥 2 + 20𝑥 − 7 = 0
𝑥 + 7
5𝑥 − 2
= 20𝑥
= −17𝑥
3𝑥 3𝑥 2 21𝑥
𝑥 5𝑥 2 −2𝑥
−
−
1 −1𝑥 −7
3 −15𝑥 6
5𝑥 − 2 𝑥 − 3 = 0
5𝑥 − 2 = 0
𝑥−3 =0
+2 + 2
+3 + 3
5𝑥 = 2
𝒙=𝟑
5
5
𝟐
𝒙=
𝟓
3𝑥 − 1 𝑥 + 7 = 0
3𝑥 − 1 = 0
𝑥+7 =0
+1 + 1
−7 − 7
3𝑥 = 1
𝒙 = −𝟕
3
3
𝟏
𝒙=
𝟑
4.4 FACTORING QUADRATICS IN STANDARD FORM
EXAMPLE: Factor then solve the following quadratic
equations.
1. 2𝑥 2 + 11𝑥 + 12 = 0
2. 3𝑥 2 − 10𝑥 − 8 = 0
3𝑥 + 2
2𝑥 + 3
= −10𝑥
= 11𝑥
𝑥 3𝑥 2 2𝑥
𝑥 2𝑥 2 3𝑥
−
+
12
4 −12𝑥 −8
4 8𝑥
2𝑥 + 3 𝑥 + 4 = 0
2𝑥 + 3 = 0
𝑥+4 =0
−3 − 3
−4 − 4
2𝑥 = −3
𝒙 = −𝟒
2
2
𝟑
𝒙=−
𝟐
3𝑥 + 2 𝑥 − 4 = 0
3𝑥 + 2 = 0
𝑥−4 =0
−2 − 2
+4 + 4
3𝑥 = −2
𝒙=𝟒
3
3
𝟐
𝒙=−
𝟑
4.4 FACTORING QUADRATICS IN STANDARD FORM
EXAMPLE: Factor then solve the following quadratic
equations.
1. 15𝑥 2 − 2𝑥 − 8 = 0
2. 9𝑥 2 − 13𝑥 − 10 = 0
9𝑥 + 5
3𝑥 + 2
= −13𝑥
= −2𝑥
5𝑥 15𝑥 2 10𝑥
𝑥 9𝑥 2 5𝑥
−
−
2 −18𝑥 −10
4 −12𝑥 −8
3𝑥 + 2 5𝑥 − 4 = 0
3𝑥 + 2 = 0 5𝑥 − 4 = 0
−2 − 2
+4 + 4
3𝑥 = −2
5𝑥 = 4
3
3
5
5
𝟐
𝟒
𝒙=−
𝒙=
𝟑
𝟓
9𝑥 + 5 𝑥 − 2 = 0
9𝑥 + 5 = 0
𝑥−2 =0
−5 − 5
+2 + 2
9𝑥 = −5
𝒙=𝟐
9
9
𝒙=
𝟓
−
𝟗
IN CLASS WORK #4:
Solving Quadratics in Factored Form
Previous Assignments:
#1: Graphing Quadratics in Standard Form WS #1
#2: Graphing Quadratics in Vertex Form WS #2
#3: Solving Quadratics in Factored From WS #3
Slide 9
TODAY IN ALGEBRA 2.0…
Warm Up: Zeros in Factored Form
Learning Goal 1: 4.4 You will solve
quadratics in factored form.
Independent Practice
WARM UP: Factor then solve the following quadratic
equations.
1. 𝑥 2 − 16𝑥 + 64 = 0
64
∗
−𝟖 −𝟖
+
−16
𝑥−8 𝑥−8 =0
𝑥−8 =0
+8 + 8
𝒙=𝟖
𝑥−8 =0
+8 + 8
𝒙=𝟖
2. 𝑥 2 − 11𝑥 + 30 = 0
30
∗
−𝟓 −𝟔
+
−11
𝑥−5 𝑥−6 =0
𝑥−5 =0
+5 + 5
𝒙=𝟓
𝑥−6 =0
+6 + 6
𝒙=𝟔
REMEMBER WHY FACTORED FORM IS IMPORTANT…
Below is the graph 𝑦 = 𝑥 2 + 2𝑥 − 8
ZEROS: Where the graph goes
through the x-axis
𝑥 = −4 𝑥 = 2
We can rewrite the equation
using the zeros:
𝑦 = 𝑥 2 + 2𝑥 − 8
𝑦 = (𝑥 + 4)(𝑥 − 2)
This is what you called
FACTORED FORM.
*Notice the signs inside the
parenthesis are opposite…
4.4 FACTORING QUADRATICS IN STANDARD FORM
TRINOMIAL FACTORING RULES:
If
𝑎𝑥 2 + 𝑏𝑥 + 𝑐
then ( +
)( +
If
𝑎𝑥 2 − 𝑏𝑥 + 𝑐
then ( −
)( −
Factored form have
the same signs.
)
If
𝑎𝑥 2 + 𝑏𝑥 − 𝑐
then ( +
)( −
)
)
If
𝑎𝑥 2 − 𝑏𝑥 − 𝑐
then ( +
)( −
)
Factored form have
the different signs.
4.4 FACTORING QUADRATICS IN STANDARD FORM
EXAMPLE: Factor then solve the following quadratic
equations.
1. 6𝑥 2 − 7𝑥 + 2 = 0
2. 3𝑥 2 + 5𝑥 − 8 = 0
3𝑥 + 8
3𝑥 − 2
= 5𝑥
= −7𝑥
𝑥 3𝑥 2 8𝑥
2𝑥 6𝑥 2 −4𝑥
−
−
1 −3𝑥 −8
1 −3𝑥 2
3𝑥 − 2 2𝑥 − 1 = 0
3𝑥 − 2 = 0 2𝑥 − 1 = 0
+1 + 1
+2 + 2
2𝑥 = 1
5𝑥 = 2
2
2
5
5
𝟏
𝟐
𝒙=
𝒙=
𝟓
𝟐
3𝑥 + 8 𝑥 − 1 = 0
3𝑥 + 8 = 0
𝑥−1 =0
−8 − 8
+1 + 1
3𝑥 = −8
𝒙=𝟏
3
3
𝟖
𝒙=−
𝟑
4.4 FACTORING QUADRATICS IN STANDARD FORM
EXAMPLE: Factor then solve the following quadratic
equations.
1. 5𝑥 2 − 17𝑥 + 6 = 0
2. 3𝑥 2 + 20𝑥 − 7 = 0
𝑥 + 7
5𝑥 − 2
= 20𝑥
= −17𝑥
3𝑥 3𝑥 2 21𝑥
𝑥 5𝑥 2 −2𝑥
−
−
1 −1𝑥 −7
3 −15𝑥 6
5𝑥 − 2 𝑥 − 3 = 0
5𝑥 − 2 = 0
𝑥−3 =0
+2 + 2
+3 + 3
5𝑥 = 2
𝒙=𝟑
5
5
𝟐
𝒙=
𝟓
3𝑥 − 1 𝑥 + 7 = 0
3𝑥 − 1 = 0
𝑥+7 =0
+1 + 1
−7 − 7
3𝑥 = 1
𝒙 = −𝟕
3
3
𝟏
𝒙=
𝟑
4.4 FACTORING QUADRATICS IN STANDARD FORM
EXAMPLE: Factor then solve the following quadratic
equations.
1. 2𝑥 2 + 11𝑥 + 12 = 0
2. 3𝑥 2 − 10𝑥 − 8 = 0
3𝑥 + 2
2𝑥 + 3
= −10𝑥
= 11𝑥
𝑥 3𝑥 2 2𝑥
𝑥 2𝑥 2 3𝑥
−
+
12
4 −12𝑥 −8
4 8𝑥
2𝑥 + 3 𝑥 + 4 = 0
2𝑥 + 3 = 0
𝑥+4 =0
−3 − 3
−4 − 4
2𝑥 = −3
𝒙 = −𝟒
2
2
𝟑
𝒙=−
𝟐
3𝑥 + 2 𝑥 − 4 = 0
3𝑥 + 2 = 0
𝑥−4 =0
−2 − 2
+4 + 4
3𝑥 = −2
𝒙=𝟒
3
3
𝟐
𝒙=−
𝟑
4.4 FACTORING QUADRATICS IN STANDARD FORM
EXAMPLE: Factor then solve the following quadratic
equations.
1. 15𝑥 2 − 2𝑥 − 8 = 0
2. 9𝑥 2 − 13𝑥 − 10 = 0
9𝑥 + 5
3𝑥 + 2
= −13𝑥
= −2𝑥
5𝑥 15𝑥 2 10𝑥
𝑥 9𝑥 2 5𝑥
−
−
2 −18𝑥 −10
4 −12𝑥 −8
3𝑥 + 2 5𝑥 − 4 = 0
3𝑥 + 2 = 0 5𝑥 − 4 = 0
−2 − 2
+4 + 4
3𝑥 = −2
5𝑥 = 4
3
3
5
5
𝟐
𝟒
𝒙=−
𝒙=
𝟑
𝟓
9𝑥 + 5 𝑥 − 2 = 0
9𝑥 + 5 = 0
𝑥−2 =0
−5 − 5
+2 + 2
9𝑥 = −5
𝒙=𝟐
9
9
𝒙=
𝟓
−
𝟗
IN CLASS WORK #4:
Solving Quadratics in Factored Form
Previous Assignments:
#1: Graphing Quadratics in Standard Form WS #1
#2: Graphing Quadratics in Vertex Form WS #2
#3: Solving Quadratics in Factored From WS #3