Question

Use factor theorem to verify that the following polynomial q(x) is a factor of p(x)

$p\left(x\right)=x^5-x^4-4x^2-2x+4,q\left(x\right)=x-2$

• A. True
• B. False

Answer 1

The correct option is A True

The zero of $q\left(x\right)=x-2$ is 2 and $p\left(x\right)=x^5-x^4-4x^2-2x+4.$

Then,

$p\left(2\right)=(2{)}^5-(2{)}^4-4(2{)}^2-2(2)+4$
$p\left(2\right)=32-16-16-4+4=0$

So, by Factor theorem, $q\left(x\right)=x-2$ is factor of $p\left(x\right)=x^5-x^4-4x^2-2x+4.$