FOUNDATIONS OF MATH 10
Chapter 5 - Day 8: FACTORING SPECIAL TRINOMIALS (Part 2)
PERFECT SQUARE TRINOMIALS
example: Use algebra tiles to factor x2 + 6x + 9 .
x
+ 3
The algebra tiles form a square.
x
x2
x x x
x
x
x
111
111
111
The dimensions of the square are (x + 3).
+
3
Answer:
The area of the large square is (x + 3)2 .
x2 + 6x + 9 = (x + 3)2
A perfect square trinomial is a trinomial that can be written as a square.
x
2
x + 6x + 9 is a perfect square trinomial.
o The first term is a square, x2 .
x
+ 3
x2
3x
3x
32
2
o The last term is a square, 3 .
+
o The middle term is in two parts, each the product
of the base from the first and last terms.
3
x2 + 6x + 9 can be written as (x)2 + 2(x)(3) + (3)2 which factors into (x + 3)2 .
FACTORING A PERFECT SQUARE TRINOMIAL:
Any expression written in the form a2 +2ab + b2 is a perfect square trinomial.
a2 + 2ab + b2 = (a + b)2
example: Factor x2 − 22x + 121
o Write it as a2 +2ab + b2 .
o Use the pattern with x as a and −11 as b.
Answer:
x2 − 22x + 121 = (x − 11)2
x2 +
−22x + 121
(x)2 + 2(x)(−11) + (−11)2
(x + −11)2
Chapter 5 - Day 8: FACTORING SPECIAL TRNOMIALS (Part 2)
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FACTORING A PERFECT SQUARE TRINOMIAL:
Expressions in the form a2 +2ab + b2 or a2 −2ab + b2 are perfect square trinomial.
a2 + 2ab + b2 = (a + b)2
a2 − 2ab + b2 = (a − b)2
exercises: Which of these polynomials are perfect square trinomials?
Factor completely if possible.
Remember to look for the greatest common factor first.
a)
4x2 + 12x + 9
b)
16m2 + 40mn + 25n2
c)
2c2 − 24c + 72
d)
9k2 + 36k + 36
e)
y2 − 20y + 64
f)
4x2 − 37x + 9
g)
x4 − 18x2 + 81
h)
x2 + 3x + 9
[Answers: (2x + 3)2, (4m + 5n)2, 2(c − 6)2, 9(k + 2)2, (y − 16)(y − 4), (4x − 1)(x − 9), (x + 3)2(x − 3)2, NF]