Objective The student will be able to:

1
ObjectiveThe student will be able to
factor trinomials with grouping. SOL A.12
Designed by Skip Tyler, Varina High School
2
Factoring ChartThis chart will help you to
determine which method of factoring to
use.Type Number of Terms

• 1. GCF 2 or more
• 2. Diff. Of Squares 2
• 3. Trinomials 3

3
Review (y 2)(y 4)
y2
First terms Outer terms Inner terms Last
terms Combine like terms. y2 6y 8
y 2
y
4
4y
2y
y2
2y
8
4y
8
In this lesson, we will begin with y2 6y 8 as
our problem and finish with (y 2)(y 4) as our
answer.
4
Here we go! 1) Factor y2 6y 8Use your
factoring chart.
Nope!

• 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.

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. Well work it out in the next few
slides.
5
1) Factor y2 6y 8Create your MAMA table.
Multiply Add8 6

• Heres your task
• What numbers multiply to 8 and add to 6? If you
  cannot figure it out right away, write the
  combinations.

6
1) Factor y2 6y 8Place the factors in the
table.
Multiply Add8 6

• 1, 8
• -1, -8
• 2, 4
• -2, -4

9, NO -9, NO 6, YES!! -6, NO
Which has a sum of 6?
We are going to use these numbers in the next
step!
7
1) Factor y2 6y 8
Multiply Add8 6

• 2, 4

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 8 Now,
group the first two terms and the last two terms.
8
We have two groups!(y2 2y)(4y 8)

• Almost done! Find the GCF of each group and
  factor it out.
• y(y 2) 4(y 2)
• (y 4)(y 2)
• Tadaaa! Theres your answer(y 4)(y 2)You
  can check it by multiplying. Piece of cake,
  huh?There is a shortcut for some problems too!
  (Im not showing you that yet)

If things are done right, the parentheses should
be the same.
Factor out the GCFs. Write them in their own
group.
9
2) Factor x2 2x 63Create your MAMA table.
Multiply Add-63 -2

• -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.
10
Replace the middle term with our working
numbers. x2 2x 63

• x2 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! Weeedoggie!
• (x 7)(x 9)

11
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.

12
2) Factor 5x2 - 17x 14 Create your MAMA table.
Multiply Add70 -17

• -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.
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(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.

14
Factor x2 3x 2

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

15
Factor 2x2 9x 10

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

16
Factor 6y2 13y 5

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

17
2) Factor 2x2 - 14x 12

• Find the GCF!
• 2(x2 7x 6)
• Now do the MAMA table!

Multiply Add6 -7
Signs need to be the same as the middle sign
since the product is positive.
-7 -5
-1, -6 -2, -3
Replace the middle term. 2x2 x 6x 6 Group
the terms.
18
2(x2 x)( 6x 6)

• Factor out the GCF
• 2x(x 1) -6(x 1)
• The parentheses are the same! Weeedoggie!
• 2(x 6)(x 1)
• Dont forget to follow your factoring chart when
  doing these problems. Always look for a GCF
  first!!