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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 6: Q. 455 (page 638)

In the following exercises, factor completely.
$x^{3} + 125$

Short Answer

Expert verified

On factoring, we get $(x + 5) (x^{2} - 5 x + 25)$ .

Step by step solution

01

Step 1. Given information.

Consider the given question,

$x^{3} + 125$

Write using the sum of cubes pattern,

$= x^{3} + 5^{3}$

Factor out,

role="math" localid="1644846379734" $= (x + 5) (x^{2} - 5 x + 25)$

02

Step 2. Check the answers.

Check by multiplying,

$= (x + 5) (x^{2} - 5 x + 25) = x^{3} - 5 x^{2} + 25 x + 5 x^{2} - 25 x - 125 = x^{3} - 125$

This is true.

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