Q.333. - Intermediate Algebra

Question

Use the remainder theorem to find the remainder.

$f\left(x\right)=7x^2-5x-8$ divided by $x-1$.

Step-by-Step Solution

Answer

The solution is $-6$.

Step 1. Given information.

$f\left(x\right)=7x^2-5x-8$ is divided by $x-1$.

Step 2. To find the remainder.

Write the divisor $x-1$ in the form $x-c$ as $x-\left(1\right)$, so $c=1$.

Substitute $x=1$ in $f\left(x\right)=7x^2-5x-8$.

$$\begin{gathered} f\left(1\right)=7{\left(1\right)}^2-5\left(1\right)-8 \\ \Rightarrow 7-5-8 \\ \Rightarrow -6 \end{gathered}$$

Step 3. Simplified answer.

Hence, the remainder is $-6$.