Question

If $x^3-5x^2+7$ is divided by $(x+2)$, then the remainder is

• A. $-21$
• B. $-20$
• C. $-17$
• D. $-25$

Answer 1

The correct option is A $-21$

let $f\left(x\right)=x^3-5x^2+7$
Now by remainder theorem, when $f\left(x\right)$ is divided by $(x-a)$, then remainder is equal to $f\left(a\right)$.
Similarly, in this case we have remainder $f(-2)$
$f(-2)=(-2{)}^3-5(-2{)}^2+7=-8-20+7=-21$