Transcript Chapter 10.1 Adding & Subtracting Polynomials

Solving Quadratics
Factoring Trinomials using
the Punnett’s Square
Factoring
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1
Trinomials
Factoring Steps:
1. Factor out the GCF other than 1.
2. Set up Diamond Problem
3. Set up Punnett's Square to find common
factors
4.Bring down GCF & Factors
*If the expression can’t be factored at all,
then it’s Prime and need to use another
method to solve.
5. Set each factor equal to zero and solve.
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2
2
Trinomials
4x  32x  28

8x
7 x
1x
7

7
4 1 x 22  8x 7
x  7 
x
1.
 1
2.
3.
 x  7   x  1
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4.
Factor out the GCF other
than 1
Set up Diamond Problem
Set up Punnett's Square
to find common factors
Bring down GCF & Factors
3
Trinomials
5. Set each factor equal to zero and solve.
*Not a factor
because it
doesn’t have
an x.


4 x  7 x 1
x 1  0
1 1
x 7 0
7
7
x  7
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
AND
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x  1
4
Trinomials
2
2x  26x  72

13x
9x 4x
36

2 1 x 22 13x 36
x
x
9
 4
1.
x  9 x  4 
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2.
3.
4.
Factor out the GCF other
than 1
Set up Diamond Problem
Set up Punnett's Square
to find common factors
Bring down GCF & Factors
5
Trinomials
5. Set each factor equal to zero and solve.
*Not a factor
because it
doesn’t have
an x.


2 x 9 x 4
x 40
4 4
x 90
9
9
x  9
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
AND
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x  4
6
2
Trinomials
x  7x  12
 1 x  7x 12
12
x  3 
x
 4
7 x
3x 4x
12
2
1.
2.
3.
 x  3 x  4 
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4.
Factor out the GCF
Set up Diamond Problem
Set up Punnett's Square
to find common factors
Bring down GCF & Factors
7
Trinomials
5. Set each factor equal to zero and solve.
 x  3 x  4 
x 40
4 4
x 3  0
3
3
x  3
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AND
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x  4
8
Trinomials
2
x  12x  35

1 x 2 12x 35
x
x

7
* Note : When the first number is a negative, factor out the (- ) sign
 5
1.
 x  7  x  5 
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12x
7 x 5x
35
2.
3.
4.
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Factor out the GCF other
than 1
Set up Diamond Problem
Set up Punnett's Square
to find common factors
Bring down GCF & Factors
9
Trinomials
5. Set each factor equal to zero and solve.
 x  7  x  5 
x 5  0
5 5
x 7  0
7
7
x 7
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AND
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x 5
10
Trinomials
2
3x  12x  35

3x 2 10x 8
3x
x
4


24
* Note : When the first number is a negative, factor out the (- ) sign
 2
1.
 x  4 3x  2
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10x
12x
2x
2.
3.
4.
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Factor out the GCF other
than 1
Set up Diamond Problem
Set up Punnett's Square
to find common factors
Bring down GCF & Factors
11
Trinomials
5. Set each factor equal to zero and solve.
 x  4 3x  2
3x  2  0
2 2
3x   2
3
3
x 40
4
4
x  4
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AND
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2
x 
3
12