Question

If $(x+1)$ and $(x-1)$ are factors of $m{x}^3+x^2-2x+n$, find the value of $m$ and $n$.

Answer 1

Let, $f\left(x\right)=m{x}^3+x^2-2x+n$

Since $(x+1)$ is a factor of $f\left(x\right)$,

then $f(-1)=0$

$\Rightarrow -m+1+2+n=0$

$\Rightarrow m-n=3$........(1)

Since $(x-1)$ is a factor of $f\left(x\right)$,

then $f\left(1\right)=0$

$\Rightarrow m+1-2+n=0$

$\Rightarrow m+n=1$.........(2)

Solving from (1) and (2) we get $m=2$ and $n=-1$