Question

The value of p for which $(x-2)$ is a factor of polynomial $x^4-x^3+2x^2-px+4$ is:

• A. 10
• B. 9
• C. 4
• D. -10

Answer 1

The correct option is A 10

$p\left(x\right)=x^4-x^3+2x^2-px+4$

Since $x-2$ is a factor of $p\left(x\right)$,

For $x-2=0$, i.e; $x=2$, $p\left(x\right)=0$

So, $p\left(2\right)=2^4-2^3+2(2{)}^2-p(2)+4=0$

$\Rightarrow 16-8+8-2p+4=0$

$\Rightarrow 2p=20$

$\Rightarrow p=+10$