Page 128 - Math Course 2 (Book 1)

Perfect Square Trinomials

Factor Completely
Let’s Begin
Examples

Factor Perfect Square Trinomials Factor 6x – 96.
2
First check for a GCF. Then, since the polynomial
Examples has two terms, check for the difference of squares.

2
2
6x – 96 = 6(x – 16) 6 is the GCF.
2
Determine whether 25x – 30x + 9 is a perfect
square trinomial. If so, factor it. = 6(x – 4 ) x = x • x and
2
2
2
16 = 4 • 4
1. Is the f rst term a perfect square?
2
2
Yes, 25x = (5x) . = 6(x + 2)(x – 2) Factor the
difference of
2. Is the last term a perfect square? squares.
2
Yes, 9 = 3 .
3. Is the middle term equal to 2(5x)(3)? Answer 6(x + 2)(x – 2)
Yes, 30x = 2(5x)(3).
2
25x – 30x + 9
Answer
is a perfect square trinomial. 2
Factor 16y + 8y – 15.
2
2
2
25x – 30x + 9 = (5x) – 2(5x)(3) + 3 This polynomial has three terms that have a
Write as GCF of 1. While the f rst term is a perfect square,
2
2
2
a – 2ab + b2. 16y = (4y) , the last term is not. Therefore, this is
not a perfect square trinomial.
= (5x – 3) 2 Factor using the
2
pattern. This trinomial is in the form ax + bx + c. Are there
two numbers m and n whose product is 16 • –15 or
–240 and whose sum is 8? Yes, the product of 20
and –12 is –240 and their sum is 8.
2
Determine whether 49y + 42y + 36 is a perfect
square trinomial. If so, factor it. 16y + 8y – 15 = 16y + mx + nx – 15
2
2
• Write the pattern
1. Is the f rst term a perfect square?
2
2
Yes, 49y = (7y) . = 16y + 20y – 12y – 15
2
• m = 20 and n = –12
2. Is the last term a perfect square?
2
Yes, 36 = 6 . = (16y + 20y) + (–12y – 15)
2
• Group terms with common factors.
3. Is the middle term equal to 2(7y)(6)?
No, 42y ≠ 2(7y)(6). = 4y(4y + 5) – 3(4y + 5)
• Factor out the GCF from each
grouping.
2
49y + 42y + 36
Answer
is not a perfect square trinomial. = 4y(4y + 5) – 3(4y + 5)
• Factor out the GCF from each
grouping.
= (4y + 5)(4y – 3)
• 4y + 5 is the common factor.

Answer (4y + 5)(4y – 3)

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