Factoring pst

1. FACTORING
POLYNOMIALS

2. Objective
The student will be able to:
factor perfect square
trinomials.
Designed by Skip Tyler, Varina High School

3. Review: Part I
Multiply.
1. (x + 7)
2
=
2. (x – 2)
2 =
3. (5x + 2y)
2=
4. (2x – 9y)
2=
5. (4x + 5y)(4x – 5y)=
6. (m
2
+ 2n)(m
2
– 2n)=

x
2
– 4x + 4
x
2
+ 14x + 49
25x
2
+ 20xy + 4y
2
4x
2
– 36xy + 81y
2
16x
2
– 25y
2
m
4
– 4n
2

4. Determine the pattern
1
4
9
16
25
36
…
= 1
2
= 2
2
= 3
2
= 4
2
= 5
2
= 6
2
These are perfect squares!
You should be able to list
the first 15 perfect
squares in 30 seconds…
Perfect squares
1, 4, 9, 16, 25, 36, 49, 64, 81,
100, 121, 144, 169, 196, 225

5. Find the factors
x
2
– 4x + 4
x
2
+ 14x + 49
25x
2
+ 20xy + 4y
2
4x
2
– 36xy + 81y
2
16x
2
– 25y
2
m
4
– 4n
2
•Factors
=(x + 7)
2
=(x + 7) (x + 7)
=(x – 2)
2
=(x – 2)(x – 2)
=(5x + 2y)(5x + 2y)
=(2x – 9y) (2x – 9y)

=(4x + 5y)(4x – 5y)
=(m
2
+ 2n)(m
2
– 2n)

6. Factoring Chart
This 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

7. First terms:
Outer terms:
Inner terms:
Last terms:
Combine like terms.
y
2
+ 4y + 4
y
2
+2y
+2y
+4
Review: Multiply (y + 2)
2
(y + 2)(y + 2)
Do you remember these?
(a + b)
2
= a
2
+ 2ab + b
2
(a - b)
2
= a
2
– 2ab + b
2
Using the formula,
(y + 2)
2
= (y)
2
+ 2(y)(2) + (2)
2
(y + 2)
2
= y
2
+ 4y + 4
Which one is quicker?

8. 1) Factor x
2
+ 6x + 9
Does this fit the form of our
perfect square trinomial?
2)Is the first term a perfect
square?
Yes, a = x
2)Is the last term a perfect
square?
Yes, b = 3
6)Is the middle term twice the
product of the a and b?
Yes, 2ab = 2(x)(3) = 6x
Perfect Square Trinomials
(a + b)
2
= a
2
+ 2ab + b
2
(a - b)
2
= a
2
– 2ab + b
2
Since all three are true,
write your answer!
(x + 3)
2
You can still
factor the other way
but this is quicker!

9. 2) Factor y
2
– 16y + 64
Does this fit the form of our
perfect square trinomial?
2)Is the first term a perfect
square?
Yes, a = y
2)Is the last term a perfect
square?
Yes, b = 8
6)Is the middle term twice the
product of the a and b?
Yes, 2ab = 2(y)(8) = 16y
Perfect Square Trinomials
(a + b)
2
= a
2
+ 2ab + b
2
(a - b)
2
= a
2
– 2ab + b
2
Since all three are true,
write your answer!
(y – 8)
2

10. 3) Factor 4p
2
+ 4p + 1
Does this fit the form of our
perfect square trinomial?
2)Is the first term a perfect
square?
Yes, a = 2p
2)Is the last term a perfect
square?
Yes, b = 1
6)Is the middle term twice the
product of the a and b?
Yes, 2ab = 2(2p)(1) = 4p
Perfect Square Trinomials
(a + b)
2
= a
2
+ 2ab + b
2
(a - b)
2
= a
2
– 2ab + b
2
Since all three are true,
write your answer!
(2p + 1)
2
=(2p + 1)
2

11. 4) Factor 25x
2
– 110xy + 121y
2
Does this fit the form of our perfect
square trinomial?
2)Is the first term a perfect
square?
Yes, a = 5x
4)Is the last term a perfect
square?
Yes, b = 11y
6)Is the middle term twice the
product of the a and b?
Yes, 2ab = 2(5x)(11y) = 110xy
Perfect Square Trinomials
(a + b)
2
= a
2
+ 2ab + b
2
(a - b)
2
= a
2
– 2ab + b
2
Since all three are true,
write your answer!
(5x – 11y)
2

12. Factor the following:
•g
2
– 24g + 144=
•m
2
+ 10m + 25
•4a
2
– 24a+ 36
FACTORING
POLYNOMIALS
Factor the following:
=(g-12 ) (g-12 )
= (m+5)(m+5)
= (2m-6)(2a-6)

13. Factor m
2
– 12m + 36
•(m – 6)(m + 6)
•(m – 6)
2
•(m + 6)
2
•(m – 18)
2

14. Factor 2r
2
+ 12r + 18
•prime
•2(r
2
+ 6r + 9)
•2(r – 3)
2
•2(r + 3)
2
•2(r – 3)(r + 3)
Don’t forget to factor the
GCF first!

15. Review
Factor 9k
2
+ 12k + 4
•(3k + 2)
2
•(3k – 2)
2
•(3k + 2)(3k – 2)
•I’ve got no clue…I’m lost!
=(3k + 2) (3k + 2)
=(3k – 2) (3k – 2)
=(3k + 2)(3k – 2)

16. Find the factors:
=
=
=
=
•x² + 6x + 9
•9m² - 6m + 1
•25s² - 20s + 4
•x² + 2xy + y²
(x + 3)²
(3m - 1)²
(5s - 2)²
(x + y)²
=(x + 3) (x + 3)
=(3m - 1) (3m - 1)
=(5s - 2) (5s - 2)
=(x + y) (x + y)

17. Find the complete factors:
=
=
=
=
1.4x² + 4x + 1
3.25s² - 60s + 36
5.27m² - 18m +3
8.8x² -72xy + 162y²
=(x + 3) (x + 3)
=(3m - 1) (3m - 1)
=(5s - 2) (5s - 2)
=(x + y) (x + y)