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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 5.89 (page 549)

Use the Remainder Theorem to find the remainder when $f (x) = x^{3} + 4 x + 15$ is divided by $x + 2$

Short Answer

Expert verified

The remainder is $- 1$

Step by step solution

01

Step 1. Given information

$f (x) = x^{3} + 4 x + 15$ is divided by $x + 2$

02

Step 2. Find the remainder

To use the Remainder Theorem, we must use the divisor in the $x - c$ form.

We can write the divisor $x + 2$ as $x - (- 2)$

So our $c$ is $- 2$

To find the remainder, we evaluate $f (c)$ which is $f (- 2)$

To evaluate $f (- 2)$ substitute $x = - 2$

role="math" localid="1646707102565" $f (x) = (x^{3} + 4 x + 15) f (- 2) = ({(- 2)}^{3} + 4 (- 2) + 15) f (- 2) = - 1$

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