Esse n t i a l U n d e r st a n d i n g Factoring a polynom ial reverses the m ultiplication
process. W hen factoring a m onom ial from a polynom ial, th e first step is to find the
greatest co m m o n factor (GCF) of th e p olynom ial’s term s.Why use th e fa c to rs
5 a n d x to fo rm th e
GCF, b u t n o t 3?
Both 5 and x are factors
of every te rm o f th e
p o ly n o m ia l, b u t 3 is o n ly
a fa c to r o f th e last te rm.
Fi n d i n g t h e Gr e a t e st Co m m o n Fact o r
What is the GCF of the terms of 5 x 3 + 2 5 x 2 + 45x?List th e p rim e factors of each term. Identify th e factors co m m o n to all term s.
5x3 = 5 • x • x • x
25x2 = 5 • 5 • x • x
45x = 3 • 3 • 5 • x
The GCF is 5 • x, o r 5x...jfr Got It? 2. W hat is th e GCF of th e term s of 3x4 - 9x2 — 12x?Remember to list only
the prime factors of
the variables.O nce you find th e GCF of a polynom ial’s term s, you can factor it out of the polynom ial.Fact o r i n g Ou t a M o n o m i al
What is the factored form of 4 x 5 — 2 4 x 3 + 8x?To fa c to r th e p o ly n o m ia l,
first factor each term.Find th e GCF o f th e
three terms.4x5 =2*2*x*x*x*x*x
24x3 = 2*2*2*3*x*x*x
8x = 2 • 2 • 2 • x
The GCF is 2 • 2 • x, or 4x.Factor o u t th e GCF fro m
each te rm. Then fa c to r it
out of the polynomial.4 x 5 - 2 4 x 3 + 8 x = 4 x ( x 4 ) + 4 x ( - 6 x 2) + 4 x ( 2 )
= 4x(x4 - 6x2 + 2)The factored form of the polynomial is
4x(x4 - 6x2 + 2).Got It? 3. a. W hat is th e factored form of 9x6 + 15x4 + 12x2?
b. Reasoning W hat is - 6 x 4 - 18x3 - 12x2 w ritten as th e p ro d u c t of a
polynomial with positive coefficients and a monomial?PowerAlgebra.com.— _
Lesso n 8-2 Multiplying and Factoring 493