Question

The remainder when $4x^3+2x^2-5x+7$ is divided by $x-2$ is

• A. $-8$
• B. $-37$
• C. $37$
• D. $8$

Answer 1

The correct option is C $37$

Let $f\left(x\right)=4x^3+2x^2-5x+7$

According to remainder theorem, if a polynomial $f\left(x\right)$ is divided by a linear function $x-k$, then the remainder is $f\left(k\right)$.

The remainder when $f\left(x\right)$ is divided by $x-2$ is
$f\left(2\right)=4(2{)}^3+2(2{)}^2-5\left(2\right)+7=37$