Warm Up
Factor the polynomial
using the distributive
method.
5
2
21𝑝𝑟 + 7𝑟 − 14𝑟 𝑝
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
General to Vertex
Method
Completing the
Square
General to Factored By Grouping
Review: (y + 2)(y + 4)
First terms: y2
Outer terms: +4y
Inner terms: +2y
Last terms: +8
Combine like terms.
y2 + 6y + 8
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
M
A
Factor y2 + 6y + 8
Create your MAMA table.
Product of the
first and last
coefficients
Multiply
+8
Add
+6
Middle
coefficient
Here’s your task…
What numbers multiply to +8 and add to
+6? If you cannot figure it out right away,
write the combinations.
1) Factor y2 + 6y + 8
Place the factors in the table.
Multiply
+8
Which has
a sum
of +6?
+1, +8
-1, -8
+2, +4
-2, -4
Add
+6
+9, NO
-9, NO
+6, YES!!
-6, NO
We are going to use these numbers in the next step!
1) Factor
Multiply
+8
+2, +4
2
y
+ 6y + 8
Add
+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 + 8
Now, group the first two terms and the last two
terms.
We have two groups!
(y2 + 2y)(+4y + 8)
Almost done! Find the GCF of each group and factor it
out.
If things are done
right, the parentheses
y(y + 2) +4(y + 2)
should be the same.
Factor out the
GCF’s. Write them
in their own group.
(y + 4)(y + 2)
Tadaaa! There’s your answer…(y + 4)(y + 2)
You can check it by multiplying. Piece of cake, huh?
Example 2
• Factor x2 – 2x – 63
M
A
2) Factor x2 – 2x – 63
Create your MAMA table.
Product of the
first and last
coefficients
Signs need to
be different
since number
is negative.
Multiply
-63
-63, 1
-1, 63
-21, 3
-3, 21
-9, 7
-7, 9
Add
-2
-62
62
-18
18
-2
2
Middle
coefficient
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!
(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
M
A
2) Factor 5x2 - 17x + 14
Create your MAMA table.
Product of the
first and last
coefficients
Signs need to
be the same as
the middle
sign since the
product is
positive.
Multiply
+70
-1, -70
-2, -35
-7, -10
Add
-17
-71
-37
-17
Replace the middle term.
5x2 – 7x – 10x + 14
Group the terms.
Middle
coefficient
(5x2 – 7x) (– 10x + 14)
Factor out the GCF
x(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!
1.
2.
3.
4.
(x + 2)(x + 1)
(x – 2)(x + 1)
(x + 2)(x – 1)
(x – 2)(x – 1)
Factor x2 + 3x + 2
You try!
1.
2.
3.
4.
(2x + 10)(x + 1)
(2x + 5)(x + 2)
(2x + 2)(x + 5)
(2x + 1)(x + 10)
Factor 2x2 + 9x + 10
You try!
1.
2.
3.
4.
Factor 6y2 – 13y – 5
(6y2 – 15y)(+2y – 5)
(2y – 1)(3y – 5)
(2y + 1)(3y – 5)
(2y – 5)(3y + 1)
Homework
• Ms.Laves Worksheet - ALL