Question

If both $x+1$ and $x-1$ are factors of $a{x}^3+x^2-2x+b$, find the values of $a$ and $b$

• A. $a=2,b=1$
• B. $a=-2,b=1$
• C. $a=-2,b=-1$
• D. $a=2,b=-1$

Answer 1

The correct option is D $a=2,b=-1$

$f\left(x\right)=9x^3+x^2-2x+b$
$f\left(1\right)=0\Rightarrow a+b=1...\left(i\right)$
$f(-1)=0\Rightarrow a-b=3...\left(ii\right)$
$Solving\left(i\right)\&\left(ii\right)a=2,b=-1$