Algebra 1 Common Core Student Edition, Grade 8-9

Do the terms share
any numerical or
variable factors?
Yes. The term s have a
common numerical factor
o f 4 and a com m on
variable factor o f q.
The GCF is 4q.

Pr o b l em 2 Fact o r i n g a Po l y n o m i a l Co m p l e t e l y

What is the factored form of 4c/4 - 8c/3 + 12q2 — 24c/? Factor completely.

4 q4 - 8c/3 + 12q2 - 24 q = 4c/(c/3 - 2c/2 + 3q - 6) Factor out the GCF.

= 4q[q2{q - 2) + 3(c/ - 2)] Factor by grouping.

= 4q(q2 + 3)(cy - 2) Factor again.

Go t I t? 2. What is the factored form of 6ft4 + 9ft3 + 12ft2 + 18ft? Factor completely.

Finding t he Dim ensions of a Rect ang ular Prism

Entertainment The toy shown below is made of several bars that can fold together

to form a rectangular prism or unfold to form a "ladder.” What expressions can

represent the dimensions of the toy when it is folded up? Use factoring.

Before factoring by grouping, you may need to factor out the GCF of all the terms.

r
How can you find the
prism's dimensions?
Factor th e cubic
expression for the
volume o f the prism
as th e p ro d u ct o f three
lin e a r expressions. Each
lin e a r expression is a
dimension.

Step 1

Step 2

Factor out the GCF.

6X3 + 19x2 + 15x = x(6x2 + 19x +

To factor the trinomial, find factors of ac that have sum ft.

Since ac = 90 and ft = 19, find factors of 90 that have sum 19.

BUteT ’h Hi

Factors o f 90 1,90 2, 45 3, 30 5 ,1 8 6 ,1 5 9, 10

Sum o f Factors 91 4 7

wmmm

3 3 2 3 21 19

Step 3 To factor the trinomial, use the factors you found to rewrite bx.

x(6x2 + 19x + 15) = x(6x2 + 9x + lOx + 15) Rewrite bx: 1 9x = 9x + 10x.

= x[3x(2x + 3) + 5(2x + 3)] Factor by grouping.

= x(3x + 5)(2x + 3) Distributive Property

The possible dimensions are x, 3x + 5, and 2x + 3.

You can sometimes factor to find possible expressions for the length, width, and height

of a rectangular prism.

5 3 0 Chapter 8 Po lyno m ials and Fact oring