Q.331. - Intermediate Algebra

Question

Use the remainder theorem to find the remainder.

$f\left(x\right)=x^3-4x-9$ is divided by $x+2$

Step-by-Step Solution

Answer

The solution is $-9$.

Step 1. Given information.

$f\left(x\right)=x^3-4x-9$ is divided by $x+2$.

Step 2. To find the remainder.

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

Substitute $x=-2$ in $f\left(x\right)=x^3-4x-9$.

$$\begin{gathered} f\left(-2\right)={\left(-2\right)}^3-4\left(-2\right)-9 \\ \Rightarrow -8+8-9 \\ \Rightarrow -9 \end{gathered}$$

Step 3. Simplified answer.

Hence, the remainder is $-9$.