Question

When $2x^3+3x^2-4x+k$ is divided by $x+2$, the remainder is $3$. Find the value of $k$.

• A. $-1$
• B. $1$
• C. $2$
• D. $3$

Answer 1

The correct option is A $-1$

Say $f\left(x\right)$ is divided by $g\left(x\right)$ and quotient is $h\left(x\right)$ , remainder is $r\left(x\right)$,then according to remainder theorem, we have $f\left(x\right)=g\left(x\right)\times h\left(x\right)+r\left(x\right)$
Here $f\left(x\right)=2x^3+3x^2-4x+k$ ,$g\left(x\right)=x+2$, $r\left(x\right)=3$
Therefore we get $2x^3+3x^2-4x+k=h\left(x\right)\times (x+2)+3$
putting $x=-2$ , we get $2(-8)+3\left(4\right)-4(-2)+k=h\left(x\right)\times \left(0\right)+3$
$\Rightarrow$ $-16+12+8+k=3$
$\Rightarrow$ $k+4=3$
$\Rightarrow$ $k=-1$