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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 5: Q.331. (page 552)

Use the remainder theorem to find the remainder.
$f (x) = x^{3} - 4 x - 9$ is divided by $x + 2$

Short Answer

Expert verified

The solution is $- 9$ .

Step by step solution

01

Step 1. Given information.

$f (x) = x^{3} - 4 x - 9$ is divided by $x + 2$ .

02

Step 2. To find the remainder.

Write the divisor $x + 2$ in the form $x - c$ as $x - (- 2)$ , so $c = - 2$ .

Substitute $x = - 2$ in $f (x) = x^{3} - 4 x - 9$ .

$f (- 2) = {(- 2)}^{3} - 4 (- 2) - 9 鈬� - 8 + 8 - 9 鈬� - 9$

03

Step 3. Simplified answer.

Hence, the remainder is $- 9$ .

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