Factoring

ObjectiveThe student will be able to:

Factor trinomials with grouping and Trial & Error.

MM1A2f

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

y2 + 6y + 8

y +2

y

+4

y2

+4y

+2y

+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.

Here we go! 1) Factor y2 + 6y + 8

Now we will learn Trinomials! You will set up a table with the following information.

Product of the first and last coefficients

Middlecoefficient

The goal is to find two factors in the first column that add up to the middle term in the second column.

We’ll work it out in the next few slides.

1) 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.

MA

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! Create two new binomials with your variable and the values you found in

your MAMA table:

( )( )y y+ 2 + 4

1) Factor. y2 + 6y + 8Put the first and last terms into the box

as shown.

What are the factors of y2?y and y

y2

+ 8

1) Factor. y2 + 6y + 8Place the factors outside the box as shown.

y2

+ 8

y

y

What are the factors of + 8?+1 and +8, -1 and -8+2 and +4, -2 and -4

The second box works. Write the numbers on the outside of box for your solution.

1) Factor. y2 + 6y + 8Which box has a sum of + 6y?

y2

+ 8

y

y

y2

+ 8

y

y+ 1 + 2

+ 8 + 4

+ y

+ 8y + 4y

+ 2y

1) Factor. y2 + 6y + 8(y + 2)(y + 4)

Here are some hints to help you choose your factors.

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.

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.

MA

1) Factor x2 – 2x – 63

7, - 9

Multiply Add-63 -2

-2, YES!!Hang with me now! Create two new binomials with your variable and the values you found in

your MAMA table:

x2

- 63

2) Factor. x2 - 2x - 63Put the first and last terms into the box

as shown.

What are the factors of x2?x and x

2) Factor. x2 - 2x - 63 Place the factors outside the box as shown.

x2

- 63

x

x

What are the factors of - 63?Remember the signs will be different!

2) Factor. x2 - 2x - 63Use trial and error to find the correct

combination!

Do any of these combinations work?The second one has the wrong sign!

x2

- 63

x

x

+ 21

- 3

+21x

-3x x2

- 63

x

x - 7

+ 9

-7x

+9x

2) Factor. x2 - 2x - 63Change the signs of the factors!

Write your solution.(x + 7)(x - 9)

x2

- 63

x

x + 7

- 9

+7x

-9x

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.

Factor x2 + 3x + 21. (x + 2)(x + 1)2. (x – 2)(x + 1)3. (x + 2)(x – 1)4. (x – 2)(x – 1)