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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset Vaia Explanations$ Math

2nd Edition · 1240 pages

ISBN: 9780998625713

Chapter 7: Q 7.17. (page 814)

Factor: $2 x^{3} + 12 x^{2}$

Short Answer

Expert verified

The required factor is $2 x^{2} (x + 6)$ .

Step by step solution

01

Step 1. Given information.

The given polynomial is:

$2 x^{3} + 12 x^{2}$

02

Step 2. Find the GCF.

Find the GCF of $2 x^{3} and 12 x^{2}$ ,

$2 x^{3} = 2 \cdot x \cdot x \cdot x 12 x^{2} = 2 \cdot 2 \cdot 3 \cdot x \cdot x$

GCF is:

$= 2 \cdot x \cdot x = 2 x^{2}$

03

Step 3. Find the factor.

Rewrite each term as a product using the GCF,

$2 x^{2} \cdot x + 2 x^{2} \cdot 6$

Factor the GCF,

$2 x^{2} (x + 6)$

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Most popular questions from this chapter

Factor: $18 u - 36$

In the following exercises, factor completely.

$4 c^{2} + 20 c d + 81 d^{2}$

In the following exercises, solve:

$x^{2} + 9 x + 20 = 0$ .

Factor Differences of Squares

In the following exercises, factor.

$49 a^{2} - 144$

In the following exercises, factor completely.

$5 n^{3} + 320$

See all solutions

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