9.5

Factoring Trinomials

9.5 – Factoring Trinomials

Goals / “I can…”Factor trinomials

9.5 – Factoring Trinomials

Remember how to find the factors of a number.

Try 24

9.5 – Factoring Trinomials

Look at the binomials

(x + 3) (x + 8)If I multiplied them out.

x + 8x + 3x + 8 * 3 =

x + 11x + 24Notice that the middle term is the sum

of 8 and 3 and the last term is the product of 8 and 3.

2

2

9.5 – Factoring Trinomials

Using this we can factor a trinomial. It is like doing the opposite of FOIL.

9.5 – Factoring Trinomials

a + 13a + 30 What are the factors of 30?

Which factors add up to 13?

Once you find the correct combination, write the result as two binomials.

( )( )

2

Here we go! 1) Factor y2 + 6y + 8Use your factoring chart.

Do we have a GCF?

Is it a Diff. of Squares problem?

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

Nope!No way! 3 terms!

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 yy22 ++ 66y + 8y + 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 yy22 + 6y + 8 + 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!

So your answer would be

(x + 2)(x + 4)(x + 2)(x + 4)

2) Factor xx22 – 2x – 63 – 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

-62

62

-18

18

-2

2

Signs need to be different

since number is negative.

M

A

Here are some hints to help you choose your factors in

the MAMAMAMA 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.

9.5 – Factoring Trinomials

TRY:

a + 8a + 152

Multiply Add+15 +8

Factor x2 + 3x + 2

1. (x + 2)(x + 1)

2. (x – 2)(x + 1)

3. (x + 2)(x – 1)

4. (x – 2)(x – 1)

9.5 – Factoring Trinomials

What happens if the middle term is negative?

x – 11x + 18

What are the factors of 18 that add up to – 11?

2

xx

2: 6 8Example x x

xx x2

x x Factors of +8: 1 & 8

2 & 4

-1 & -8

-2 & -4

2x + 4x = 6x

1x + 8x = 9x

O + I = bx ?

-2x - 4x = -6x

-1x - 8x = -9x

-2-4

x2 6x 8

Check your answer by using FOIL

(x 2)(x 4)

(x 2)(x 4) x2 4x 2x 8F O I L

x2 6x 8

9.5 – Factoring Trinomials

TRY:

c – 9c + 20

Remember to make your MAMA

2

Multiply Add+20 -9

9.5 – Factoring Trinomials

What happens if the last term is negative?

p + 8p – 20

Now one term will be positive, one will be negative.

BE CAREFUL!!!BE CAREFUL!!!

2

9.5 – Factoring Trinomials

TRY:

x – 5x – 242

9.5 – Factoring Trinomials

Factors with two variables.Factors with two variables.This is just like the other problems but

both parts will have a variable.

9.5 – Factoring Trinomials

d + 17dg – 60g2 2