Question

If $x+1$ & $x-1$ are factors of polynomial $x^4+p{x}^3-3x^2+2x+q$ then find the value of $P\&Q$.

Answer 1

let $x^4+p{x}^3-3x^2+2x+q=f\left(x\right)$

if $x+1,x-1$ are factors of $f\left(x\right)$ then $f\left(1\right)=0,f(-1)=0$

$f\left(1\right)=p+q=0$

$f(-1)=p-q=-4$

add these 2 equations

we get $2p=-4$

$p=-2$

put p in any equation

$-2+q=0$

$q=2$