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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 183 (page 850)

In the following exercises, factor $48 z^{3} - 102 z^{2} - 45 z$

Short Answer

Expert verified

The factorization of the expression $48 z^{3} - 102 z^{2} - 45 z$ is $3 z (8 z + 3) (2 z - 5)$ .

Step by step solution

01

Step 1. Given information

Given expression is $48 z^{3} - 102 z^{2} - 45 z$

02

Step 2. Factorizing by 'ac' method.

$a 脳 c = 16 脳 (- 15) = - 240$

Factorization:

48 z^{3} - 102 z^{2} - 45 z = 3 z (16 z^{2} + 6 z - 40 z - 15) = 3 z (2 z (8 z + 3) - 5 (8 z + 3)) = 3 z (8 z + 3) (2 z - 5)

03

Step 3. Check

$3 z (8 z + 3) (2 z - 5) = 3 z (16 z^{2} + 6 z - 40 z - 15) = 48 z^{3} - 102 z^{2} - 45 z$

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