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

Answer: (A)

$-21$

Given $f\left(x\right)=x^3-5x^2+7$ and divisor is $x+2$.

We put $x+2=0$

$\therefore x=-2$

According to remainder theorem,

If $f\left(x\right)$ is divided by $x-a$, the remainder will be $f\left(a\right)$.

Here, $a=-2.$

$\therefore f(-2)=(-2{)}^3-5(-2{)}^2+7$ $=-21$