Q 5.89 - Intermediate Algebra

Question

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

Step-by-Step Solution

Answer

The remainder is $-1$

Step 1. Given information

$f\left(x\right)=x^3+4x+15$ is divided by $x+2$

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 $x-\left(-2\right)$

So our $c$ is $-2$

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

To evaluate $f\left(-2\right)$ substitute $x=-2$

$$\begin{gathered} f\left(x\right)=\left(x^3+4x+15\right) \\ f\left(-2\right)=\left({\left(-2\right)}^3+4\left(-2\right)+15\right) \\ f\left(-2\right)=-1 \end{gathered}$$