Chapter 12, Problem 10STP

To determine

To find: Remainder.

Answer to Problem 10STP

Remainder is $-1$ .

Explanation of Solution

Given information:

  $f\left(x\right)=x^3-7x+5$

Is divided by $\left(x+3\right)$

Concept:

Remainder of

  $f\left(x\right)÷\left(x-a\right)$ is $f\left(-a\right)$ .

  $f\left(x\right)=x^3-7x+5$

Is divided by $\left(x+3\right)$

Therefore,

Remainder is $f\left(-3\right)$

Therefore,

On substituting $x=-3$

We get

  $\begin{array}{l}f\left(x\right)=x^3-7x+5\\ \Rightarrow f\left(-3\right)={\left(-3\right)}^3-7\left(-3\right)+5\\ \Rightarrow f\left(-3\right)=-27+21+5\\ \Rightarrow f\left(-3\right)=-27+26\\ \Rightarrow f\left(-3\right)=-1\end{array}$

Therefore,

Remainder is $-1$ .