Transcript Factoring to Solve Quadratic Equations

Factoring to Solve Quadratic
Solve and check eachEquations
equation.
ALGEBRA 1 LESSON 10-5
(For help, go to Lessons 2-2 and 9-6.)
1. 6 + 4n = 2
2. a – 9 = 4
3. 7q + 16 = –3
5. 3p2 + 32p + 20
6. 4x2 – 21x – 18
8
Factor each expression.
4. 2c2 + 29c + 14
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Factoring to Solve Quadratic
Equations
Solutions
ALGEBRA 1 LESSON 10-5
1. 6 + 4n = 2
4n = –4
n = –1
Check: 6 + 4(–1) = 6 + (–4) = 2
a
2. 8 – 9 = 4
a
= 13
8
a = 104
Check: 104 – 9 = 13 – 9 = 4
8
3. 7q + 16 = –3
7q = –19
q = –2 5
7
5
Check: 7 (–2 ) + 16 = 7(– 19 ) + 16 = –19 + 16 = –3
7
7
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Factoring to Solve Quadratic
Equations
Solutions (continued)
ALGEBRA 1 LESSON 10-5
4. 2c2 + 29c + 14 = (2c + 1)(c + 14)
Check: (2c + 1)(c + 14) = 2c2 + 28c + c + 14 = 2c2 + 29c + 14
5. 3p2 + 32p + 20 = (3p + 2)(p + 10)
Check: (3p + 2)(p + 10) = 3p2 + 30p + 2p + 20 = 3p2 + 32p + 20
6. 4x2 – 21x – 18 = (4x + 3)(x – 6)
Check: (4x + 3)(x – 6) = 4x2 – 24x + 3x – 18 = 4x2 – 21x – 18
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Factoring to Solve Quadratic
Equations
Solve (2x + 3)(x – 4) = 0 by using the Zero Product Property.
ALGEBRA 1 LESSON 10-5
(2x + 3)(x – 4) = 0
2x + 3 = 0
x–4=0
or
2x = –3
3
x=–2
Use the Zero-Product Property.
Solve for x.
or
x=4
3
Check: Substitute – 2 for x.
Substitute 4 for x.
(2x + 3)(x – 4) = 0
[2(– 3 ) + 3](– 3 – 4)
2
2
(2x + 3)(x – 4) = 0
[2(4) + 3](4 – 4)
0
1
(0)(– 5 2 ) = 0
0
(11)(0) = 0
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Factoring to Solve Quadratic
Equations
Solve x + x – 42 = 0 by factoring.
ALGEBRA 1 LESSON 10-5
2
x2 + x – 42 = 0
(x + 7)(x – 6) = 0
Factor using x2 + x – 42
x+7=0
or
x–6=0
Use the Zero-Product Property.
x = –7
or
x=6
Solve for x.
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Factoring to Solve Quadratic
Equations
Solve 3x – 2x = 21 by factoring.
ALGEBRA 1 LESSON 10-5
2
3x2 – 2x = 21
Subtract 21 from each side.
(3x + 7)(x – 3) = 0
3x + 7 = 0
Factor 3x2 – 2x – 21.
x–3=0
or
3x = –7
7
x=– 3
Use the Zero-Product Property
Solve for x.
or
x=3
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Factoring to Solve Quadratic
Equations
1. Solve (2x – 3)(x + 2)
= 0.
ALGEBRA 1 LESSON 10-5
3
–2, 2
Solve by factoring.
2. 6 = a2 – 5a
–1, 6
3. 12x + 4 = –9x2
4. 4y2 = 25
2
3
±
–
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5
2