Question

Find the remainder when $x^3-7x^2-x+6$ is divided by $(x+2)$.

Answer 1

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

$f\left(x\right)=x^3-7x^2-x+6$

$f(-2)=(-2{)}^3-7(-2{)}^2-(-2)+6$

$=-8-7\times 4+2+6$

$=-8-28+8=-28$

$\therefore$ Remainder $=-28$