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FACTORING POLYNOMIALS
ObjectiveThe student will be able to:
factor perfect square trinomials.
Designed by Skip Tyler, Varina High School
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. (m2 + 2n)(m2 – 2n)=
x2 – 4x + 4
x2 + 14x + 49
25x2 + 20xy + 4y2
4x2 – 36xy + 81y2
16x2 – 25y2
m4 – 4n2
Determine the pattern149162536…
= 12
= 22
= 32
= 42
= 52
= 62
These are perfect squares!
You should be able to list the first 15 perfect
squares in 30 seconds…
Perfect squares1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225
Find the factors
x2 – 4x + 4
x2 + 14x + 49
25x2 + 20xy + 4y2
4x2 – 36xy + 81y2
16x2 – 25y2
m4 – 4n2
• 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)
=(m2 + 2n)(m2 – 2n)
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 23. Trinomials 3
First terms:
Outer terms:
Inner terms:
Last terms:
Combine like terms.
y2 + 4y + 4
y2
+2y+2y+4
Review: Multiply (y + 2)2
(y + 2)(y + 2)Do you remember these?(a + b)2 = a2 + 2ab + b2
(a - b)2 = a2 – 2ab + b2
Using the formula, (y + 2)2 = (y)2 + 2(y)(2) + (2)2
(y + 2)2 = y2 + 4y + 4
Which one is quicker?
1) Factor x2 + 6x + 9Does this fit the form of our
perfect square trinomial?1) Is the first term a perfect
square?Yes, a = x
2) Is the last term a perfect square?
Yes, b = 33) Is the middle term twice the
product of the a and b?Yes, 2ab = 2(x)(3) = 6x
Perfect Square Trinomials(a + b)2 = a2 + 2ab + b2
(a - b)2 = a2 – 2ab + b2
Since all three are true, write your answer!
(x + 3)2
You can still factor the other way but this is quicker!
2) Factor y2 – 16y + 64Does this fit the form of our
perfect square trinomial?1) Is the first term a perfect
square?Yes, a = y
2) Is the last term a perfect square?
Yes, b = 83) Is the middle term twice the
product of the a and b?Yes, 2ab = 2(y)(8) = 16y
Perfect Square Trinomials(a + b)2 = a2 + 2ab + b2
(a - b)2 = a2 – 2ab + b2
Since all three are true, write your answer!
(y – 8)2
3) Factor 4p2 + 4p + 1Does this fit the form of our
perfect square trinomial?1) Is the first term a perfect
square?Yes, a = 2p
2) Is the last term a perfect square?
Yes, b = 13) Is the middle term twice the
product of the a and b?Yes, 2ab = 2(2p)(1) = 4p
Perfect Square Trinomials(a + b)2 = a2 + 2ab + b2
(a - b)2 = a2 – 2ab + b2
Since all three are true, write your answer!
(2p + 1)2
=(2p + 1)2
4) Factor 25x2 – 110xy + 121y2
Does this fit the form of our perfect square trinomial?
1) Is the first term a perfect square?
Yes, a = 5x2) Is the last term a perfect
square?Yes, b = 11y
3) Is the middle term twice the product of the a and b?Yes, 2ab = 2(5x)(11y) = 110xy
Perfect Square Trinomials(a + b)2 = a2 + 2ab + b2
(a - b)2 = a2 – 2ab + b2
Since all three are true, write your answer!
(5x – 11y)2
Factor the following:1.g2 – 24g + 144= 2.m2 + 10m + 253.4a2 – 24a+ 36
FACTORING POLYNOMIALSFactor the following:
=(g-12 ) (g-12 )= (m+5)(m+5)= (2m-6)(2a-6)
Factor m2 – 12m + 36
A. (m – 6)(m + 6)B. (m – 6)2
C. (m + 6)2
D. (m – 18)2
Factor 2r2 + 12r + 18
1. prime2. 2(r2 + 6r + 9)3. 2(r – 3)2
4. 2(r + 3)2
5. 2(r – 3)(r + 3)
Don’t forget to factor the GCF first!
ReviewFactor 9k2 + 12k + 4A. (3k + 2)2
B. (3k – 2)2
C. (3k + 2)(3k – 2)D. I’ve got no clue…I’m lost!
(3k + 2) (3k + 2)(3k – 2) (3k – 2)(3k + 2)(3k – 2)
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)
Find the complete factors:=
=
=
=
1. 4x² + 4x + 1
2. 25s² - 60s + 36
3. 27m² - 18m +3
4. 8x² -72xy + 162y²
(x + 3) (x + 3)
(3m - 1) (3m - 1)
(5s - 2) (5s - 2)
(x + y) (x + y)
