Warm Up

Factor the polynomial using the distributive

method.

Factor By Grouping

Goal

• We know how to write a general quadratic in vertex form (complete the square), but now we want to write a general quadratic in factored form.

When to use which method

Result MethodGeneral to Vertex Completing the

SquareGeneral to Factored By Grouping

First terms:Outer terms:Inner terms:Last terms: Combine like terms.

y2 + 6y + 8

y2

+4y+2y+8

Review: (y + 2)(y + 4)

In this lesson, we will begin with y2 + 6y + 8 as our problem and finish with (y + 2)(y + 4) as our answer.

Steps

• 1. Factor out the GCF• 2. Set up a MAMA table

Example 1

Factor y2 + 6y + 8

Any GCF?No

Factor y2 + 6y + 8Create your MAMA table.

Multiply Add+8 +6

Product of the first and last coefficients

Middlecoefficient

Here’s your task…What numbers multiply to +8 and add to +6? If you cannot figure it out right away,

write the combinations.

M

A

1) Factor y2 + 6y + 8Place the factors in the table.

+1, +8-1, -8+2, +4 -2, -4

Multiply Add+8 +6

Which has a sum of +6?

+9, NO-9, NO+6, YES!!-6, NO

We are going to use these numbers in the next step!

1) Factor y2 + 6y + 8

+2, +4

Multiply Add+8 +6

+6, YES!!Hang with me now! Replace the middle number of the trinomial with our working numbers from the

MAMA table y2 + 6y + 8

y2 + 2y + 4y + 8Now, group the first two terms and the last two

terms.

We have two groups!(y2 + 2y)(+4y + 8)

If things are done right, the parentheses should be the same.

Almost done! Find the GCF of each group and factor it out.

y(y + 2) +4(y + 2)

(y + 4)(y + 2)Tadaaa! There’s your answer…(y + 4)(y + 2)

You can check it by multiplying. Piece of cake, huh?

Factor out the GCF’s. Write them in their own group.

Example 2

• Factor x2 – 2x – 63

2) Factor x2 – 2x – 63Create your MAMA table.

Multiply Add-63 -2

Product of the first and last coefficients

Middlecoefficient

-63, 1-1, 63-21, 3-3, 21-9, 7-7, 9

-6262-1818-2 2

Signs need to be different

since number is negative.

M

A

Replace the middle term with our working numbers.

x2 – 2x – 63x2 – 9x + 7x – 63 Group the terms.

(x2 – 9x) (+ 7x – 63)Factor out the GCF

x(x – 9) +7(x – 9)The parentheses are the same!

(x + 7)(x – 9)

Here are some hints to help you choose your factors in the

MAMA table.1) When the last term is positive, the factors

will have the same sign as the middle term.2) When the last term is negative, the factors

will have different signs.

Example 3

• 5x2 - 17x + 14

2) Factor 5x2 - 17x + 14 Create your MAMA table.

Multiply Add+70 -17

Product of the first and last coefficients

Middlecoefficient

-1, -70-2, -35-7, -10

-71-37-17

Signs need to be the same as

the middle sign since the

product is positive. Replace the middle term.

5x2 – 7x – 10x + 14Group the terms.

M

A

(5x2 – 7x) (– 10x + 14)Factor out the GCFx(5x – 7) -2(5x – 7)

The parentheses are the same! (x – 2)(5x – 7)

These will continue to get easier the more you do them.

You try! Factor x2 + 3x + 2

1. (x + 2)(x + 1)2. (x – 2)(x + 1)3. (x + 2)(x – 1)4. (x – 2)(x – 1)

You try! Factor 2x2 + 9x + 10

1. (2x + 10)(x + 1)2. (2x + 5)(x + 2)3. (2x + 2)(x + 5)4. (2x + 1)(x + 10)

You try! Factor 6y2 – 13y – 5

1. (6y2 – 15y)(+2y – 5)2. (2y – 1)(3y – 5)3. (2y + 1)(3y – 5)4. (2y – 5)(3y + 1)

Homework

• Ms.Laves Worksheet - ALL