Question

Find the remainder when $x^4+2x^3-13x^2-14x+24$ is divided by $(x+1)$. Also show that the same expression is exactly divisible by $(x-1)$.

Answer 1

Let $f\left(x\right)=x^4+2x^3-13x^2-14x+24$.

Now the remainder when $f\left(x\right)$ is divided by $(x+1)$ be

$f(-1)=1-2-13+14+24=24$.

So the required remainder is $24$.

Now the remainder when $f\left(x\right)$ is divided by $(x-1)$ be

$f\left(1\right)=1+2-13-14+24=0$.

So $f\left(x\right)$ is exactly divisible by $(x-1)$.