Q.330. - Intermediate Algebra

Question

Use the remainder theorem to find the remainder.

$f\left(x\right)=x^3-8x+7$ is divided by $x+3$.

Step-by-Step Solution

Answer

The solution is $4$.

Step 1. Given information.

$f\left(x\right)=x^3-8x+7$ is divided by $x+3$.

Step 2. Find the remainder.

Write the divisor $x+3$ in the form of $x-c$ as $x-\left(-3\right)$, so $c=-3$.

Simplify the $f\left(-3\right)$ by substituting $x=-3$ in $f\left(x\right)=x^3-8x+7$.

$$\begin{gathered} f\left(-3\right)={\left(-3\right)}^3-8\left(-3\right)+7 \\ \Rightarrow -27+24+7 \\ \Rightarrow 4 \end{gathered}$$

Step 3. Simplified answer.

Hence, the remainder is $4$.