Algebra 1 Common Core Student Edition, Grade 8-9

Will the answer have
the form (a + b)2 or
(a - b)2?
The m iddle term - 1 2 x
has a negative
coefficient, so the
factored expression w ill
have the form (a - b)2.

Pr o b l em 1 Fac t o r i n g a Pe r f e c t - Sq u a r e Tr i n o m i al

What is the factored form of x2 — 12x + 36?

x2 - I2x + 36 = x2 - 12x + 62 W rite th e last te rm as a square.

= x2 - 2(x)(6) + 62 Does m iddle term equal -labl -12x = -2(x)(6)

= (x - 6)2 Write as the square of a binomial.

^ G o t It? 1. What is the factored form of each expression?

a. x2 + 6x + 9 b. x2 — 14x + 49

Fac t o r i n g t o Fi n d a Len g t h

Computers Digital images are composed of thousands of tiny pixels rendered as

squares, as shown below. Suppose the area of a pixel is 4 x 2 + 20x + 25. What is the

length of one side of the pixel?

Pr o b l em

How can you find the
side length?
Since the pixel's area is
its side length squared,
factor the expression for
area as the square of a
binom ial. The binom ial is
the side length.

4x2 + 20x + 25 = (2x)2 + 20x + 52 W rite firs t and last term s as squares.

= (2x)2 + 2(2x)(5) + 52 Does m iddle term equal labl 20x = 2(2x)(5)

= (2x + 5)2 W rite as th e square o f a b in o m ial.

The length of one side of the pixel is 2x + 5.

G o t If? 2. You are building a square patio. The area of the patio is 16m2 - 72m + 81.

What is the length of one side of the patio?

5 2 4 Chapter 8 Polynomials and Factoring