MCR Notes 11.5 Factoring Polynomials by Grouping … Notes 11.5 Factoring Polynomials by Grouping...
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Transcript of MCR Notes 11.5 Factoring Polynomials by Grouping … Notes 11.5 Factoring Polynomials by Grouping...
MCR Notes 11.5 Factoring Polynomials by Grouping Part 2.notebook
1
January 11, 2016
11.5 Factor by Grouping Part 2
The first step in factoring a polynomial is look for a common
monomial factor. If you find one extract it. Once the
polynomial is in quadratic form use the following to split the
middle term so that you can use the grouping method to
factor. There are four possibilities, the same basic technique
works for all four.
MCR Notes 11.5 Factoring Polynomials by Grouping Part 2.notebook
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January 11, 2016
1. Given a quadratic in the form: ax2 + bx + c.
Find the factor pairs of ac that add to give you b then
write the quadratic as ax2 + b1x + b2x + c. Next you factor
using grouping.
Example: x2 + 5x + 6
(1)(6) = 6
Factor pairs are:
1, 6: 1 + 6 = 7
2, 3: 2 + 3 = 5 we will use this sum.
x2 + 2x + 3x + 6
x(x + 2) + 3(x + 2)
(x + 2)(x + 3)
MCR Notes 11.5 Factoring Polynomials by Grouping Part 2.notebook
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January 11, 2016
Example: 2x2 + 11x + 15
MCR Notes 11.5 Factoring Polynomials by Grouping Part 2.notebook
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January 11, 2016
Example: 2x2 + 7x + 5
MCR Notes 11.5 Factoring Polynomials by Grouping Part 2.notebook
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January 11, 2016
Example 1
Grade:«grade»
Subject:«subject»
Date:«date»
MCR Notes 11.5 Factoring Polynomials by Grouping Part 2.notebook
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January 11, 2016
1 You Try: x2 + 5x + 4
A (x + 2)(x + 2)
B (x + 1)(X + 4)
C (x + 2)(x + 3)
D Not factorable
MCR Notes 11.5 Factoring Polynomials by Grouping Part 2.notebook
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January 11, 2016
2. Given a quadratic in the form: ax2 - bx + c.
Find the factor pairs of ac that add to give you b then
write the quadratic as ax2 - b1x - b2x + c. Next you factor
using grouping.
Example: x2 - 8x + 15
(1)(15) = 15
Factors:
-1, -15: -1 + (-15) = -16
-3, -5: -3 + (-5) = -8
x2 - 3x - 5x + 15
x(x - 3) -5(x - 3)
(x - 3)(x - 5)
MCR Notes 11.5 Factoring Polynomials by Grouping Part 2.notebook
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January 11, 2016
Example: 3x2 - 13x + 10
MCR Notes 11.5 Factoring Polynomials by Grouping Part 2.notebook
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January 11, 2016
Example 2
Grade:«grade»
Subject:«subject»
Date:«date»
MCR Notes 11.5 Factoring Polynomials by Grouping Part 2.notebook
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January 11, 2016
1 5x2 - 11x + 6
A (x + 2)(x + 9)
B (x - 5)(x - 6)
C (5x - 6)(x - 1)
D (5x - 1)(x - 6)
MCR Notes 11.5 Factoring Polynomials by Grouping Part 2.notebook
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January 11, 2016
3. Given a quadratic in the form: ax2 + bx - c.
Find the factor pairs of ac that add to give you b then
write the quadratic as ax2 + b1x - b2x - c, where b1 is larger
and positive, and b2 is negative. Next you factor using
grouping.
Example: x2 + 2x - 8
(1)(-8) = -8
Factors: (sum)
-1, 8 (7)
1, -8 (-7)
2, -4 (-2)
x2 + 4x - 2x - 8
x(x + 4) -2(x + 4)
(x + 4)(x - 2)
MCR Notes 11.5 Factoring Polynomials by Grouping Part 2.notebook
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January 11, 2016
Example:
2x2 + 3x - 5
MCR Notes 11.5 Factoring Polynomials by Grouping Part 2.notebook
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January 11, 2016
Example 3
Grade:«grade»
Subject:«subject»
Date:«date»
MCR Notes 11.5 Factoring Polynomials by Grouping Part 2.notebook
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January 11, 2016
1 x2 + 2x - 35
A (x + 7)(x - 5)
B (x - 7)( x + 5)
C (x + 3)( x - 1)
D (x + 5)(x - 3)
MCR Notes 11.5 Factoring Polynomials by Grouping Part 2.notebook
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January 11, 2016
4. Given a quadratic in the form: ax2 - bx - c.
Find the factor pairs of ac that add to give you b then
write the quadratic as ax2 + b1x - b2x - c, where b1 is
smaller and positive, and b2 is negative. Next you factor
using grouping.
Example: x2 - 2x - 8
Factors: (sum)
-1, 8 (7)
1, -8 (-7)
x2 + 2x - 4x - 8
x(x + 2) -4(x + 2)
(x - 4)(x + 2)
MCR Notes 11.5 Factoring Polynomials by Grouping Part 2.notebook
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January 11, 2016
Example:
2x2 - 3x - 5
MCR Notes 11.5 Factoring Polynomials by Grouping Part 2.notebook
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January 11, 2016
Example 4
Grade:«grade»
Subject:«subject»
Date:«date»
MCR Notes 11.5 Factoring Polynomials by Grouping Part 2.notebook
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January 11, 2016
1 x2 - 3x - 18
A (x - 9)(x + 2)
B (x - 1)(x - 2)
C (x - 3)(x + 6)
D (x - 6)( x + 3)
MCR Notes 11.5 Factoring Polynomials by Grouping Part 2.notebook
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January 11, 2016