Question

Use factor theorem to verify that the following polynomial $q\left(x\right)$ is a factor of $p\left(x\right)$ $p\left(x\right)=x^4-x^3+x-1,q\left(x\right)=x+1$

• A. True
• B. False

Answer 1

The correct option is A True

Here,

$p\left(x\right)=x^4-x^3+x-1$ and $q\left(x\right)=x+1$

Equate $q\left(x\right)$ to $0$

$x+1=0$

$\Rightarrow x=-1$

Put the obtained value of $x$ in $p\left(x\right)$

Then,

$p(-1)=(-1{)}^4-(-1{)}^3+(-1)-1$
$=1+1-1-1=0$

So, by Factor theorem, $q\left(x\right)=x+1$ is factor of $p\left(x\right)=x^4-x^3+x-1$.