Question

When $3x^3-7x+7$ is divided by $x+2$, find the remainder.

• A. $-5$
• B. $-3$
• C. $1$
• D. $3$

Answer 1

The correct option is B $-3$

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

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 $f\left(x\right)=g\left(x\right)\times h\left(x\right)+r\left(x\right)$

Given $g\left(x\right)=x+2$

Let $h\left(x\right)=a{x}^2+bx+c$

By remainder theorem, we get

$(a{x}^2+bx+c)(x+2)+r=3x^3-7x+7$

Put $x=-2$ , we get $0+r=3(-8)-7(-2)+7$

$\Rightarrow$ $r=-24+14+7=-24+21=-3$