Question

Find the remainder using remainder theorem, when:

$5x^3+2x^2-6x+12$ is divided by $x+2$

Answer 1

According to remainder theorem, when $f\left(x\right)$ is divided by $(x+2)$, Remainder $=f(-2)$

$f\left(x\right)=5x^3+2x^2-6x+12$

$f(-2)=5(-2{)}^3+2(-2{)}^2-6(-2)+12$

$=5\times -8+2\times 4+12+12$

$=-40+32=-8$

$\therefore$ Remainder$=-8$