Objective The student will be able to:

ObjectiveThe student will be able to:

factor trinomials with grouping.

SOL: A.12

Designed by Skip Tyler, Varina High School

AIM: How do we factor trinomials AIM: How do we factor trinomials of the type xof the type x22 + bx + c? + bx + c?

• Do Now:Do Now:List all of the factors of the following numbers:List all of the factors of the following numbers:

1.1. 2424

2.2. 1212

3.3. 5454

4.4. 5656

HW Review:HW Review:

• Regents Review 10 is due tomorrow.

Big Ideas:Big Ideas:

• In earlier courses, you learned how to find the factors of whole numbers like 15.

• Since 3 x 5 = 15; 3 and 5 are factors of 15.

• You can also find the factors of some trinomials using similar methods

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.

1) Factor y2 + 6y + 8Create your MA 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 +2 and +4

(y + 2)(y + 4)

Now, let’s check our work by Now, let’s check our work by FOILing!FOILing!

(y + 2)(y + 4)

2) Factor x2 – 2x – 63Create your MA 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

Replace the factors into two binomials: x2 – 2x – 63

+7 -9

(x + 7)(x – 9)

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

MA 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)

Classwork:

• During the classwork, please work quickly and quietly in your group.

• If you have a question, please first ask a groupmate.

• If no one still knows at that point, please then ask me.

• The first group to finish will receive HW passes.

Summary:Summary:

• What is the most challenging part of factoring trinomials?

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 + 14

Group the terms.

M

A

(5x2 – 7x) (– 10x + 14)Factor out the GCF

x(5x – 7) -2(5x – 7)

The parentheses are the same! Weeedoggie!

(x – 2)(5x – 7)

Hopefully, these will continue to get easier the more you do them.

Factor 2x2 + 9x + 101. (2x + 10)(x + 1)

2. (2x + 5)(x + 2)

3. (2x + 2)(x + 5)

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

Factor 6y2 – 13y – 51. (6y2 – 15y)(+2y – 5)

2. (2y – 1)(3y – 5)

3. (2y + 1)(3y – 5)

4. (2y – 5)(3y + 1)

2) Factor 2x2 - 14x + 12

Multiply Add+6 -7

Find the GCF!

2(x2 – 7x + 6)

Now do the MAMA table!

-7

-5

Signs need to be the same as

the middle sign since the

product is positive.

Replace the middle term.

2[x2 – x – 6x + 6]

Group the terms.

-1, -6

-2, -3

2[(x2 – x)(– 6x + 6)]Factor out the GCF

2[x(x – 1) -6(x – 1)]

The parentheses are the same! Weeedoggie!

2(x – 6)(x – 1)

Don’t forget to follow your factoring chart when doing these problems. Always look for a GCF

first!!