For what value of m will the polynomial f (x)=x3+2x2+mx+5 have the same remainder when it is divided by x+1 and x−2?

The remainder theorem states that: if a polynomial, $p\left(x\right)$ is divided by $\left(x-b\right)$, then the remainder is $p\left(b\right)$. The expression, $p\left(b\right)$ is calculated by substituting $x=b$ in the polynomial, $p\left(x\right)$.