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

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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.


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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)


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January 11, 2016

Example: 2x2 + 11x + 15


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Example: 2x2 + 7x + 5


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Example 1

Grade:«grade»

Subject:«subject»

Date:«date»


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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


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January 11, 2016

2. Given a quadratic in the form: ax2 - bx + c.


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)


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Example: 3x2 - 13x + 10


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Example 2

Grade:«grade»

Subject:«subject»

Date:«date»


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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)


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January 11, 2016

3. Given a quadratic in the form: ax2 + bx - c.


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)


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January 11, 2016

Example:

2x2 + 3x - 5


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January 11, 2016

Example 3

Grade:«grade»

Subject:«subject»

Date:«date»


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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)


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January 11, 2016

4. Given a quadratic in the form: ax2 - bx - c.


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)


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January 11, 2016

Example:

2x2 - 3x - 5


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Example 4

Grade:«grade»

Subject:«subject»

Date:«date»


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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)


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January 11, 2016

mcr notes 11.5 factoring polynomials by grouping … notes 11.5 factoring polynomials by grouping...

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