Question

Find the values of $a$ and $b$ so that $x+1$ and $x-1$ are factors of $x^4+a{x}^3+2x^2-3x+b.$

Answer 1

$f\left(x\right)=x^4+{ax}^3+{2x}^2-3x+b$

$x=-1$ is factor $f(-1)=0$

$1-a+2+3+b=0$

$b-a+4=0$

$a-b=4⟶\left(1\right)$

$x=1$ is factor of $f\left(1\right)=0$

$1+a+2-3+b=0$

$a=-b⟶\left(2\right)$

$b=-a$

$2a=4$

$a=2$

$b-a=-2$

$\therefore$, $a=2$, $b=-2$