Question

When $2f^3+3f^2-1$ is divided by $f+2$, find the remainder.

• A. $-9$
• B. $-5$
• C. $-1$
• D. $2$

Answer 1

The correct option is C $-1$

The degree of dividend is $3$ and the degree of divisor is $1$ , so the degree of quotient must be $2$.

Let the quotient be $a{f}^2+bf+c$ and remainder be $r$, we have

$2f^3+3f^2-1=(a{f}^2+bf+c)(f+2)+r=a{f}^3+(2a+b)f^2+(2b+c)f+2c+r$

By comparing, we get
$a=2$, $b=-1$, $c=2$, $r=-5$
Therefore, the remainder is $-1$.