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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 7: Q 163 (page 849)

In the following exercises, the factor
$16 x^{2} - 32 x + 16$

Short Answer

Expert verified

The factorization of the expression is $16 {(x - 1)}^{2}$

Step by step solution

01

Step 1. Given information

Given expression is $16 x^{2} - 32 x + 16$

02

Step 2. Find the Greatest Common Factor.

The G.C.F is $16$

$16 (x^{2} - 2 x + 1)$

03

Step 3. Find all the factor pairs of the first term and third term.

The factors of the first term $x^{2} = x, x$

The factors of the last term $1 = 1, 1$ and $- 1, - 1$

04

Step 4. Test all the possible combinations of the factors until the correct product is found.

$16 (x - 1) (x - 1) = 16 x^{2} - 32 x + 16 16 (x + 1) (x + 1) = 16 x^{2} + 32 x + 16$

05

Step 5. Check

$16 (x - 1) (x - 1) = 16 (x^{2} - 2 x + 1) = 16 x^{2} - 32 x + 16$

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