Question

If the G.C.D of the polynomials $x^3-3x^2+px+24$ and $x^2-7x+q$ is $(x-2)$, then the value of $(p+q)$ is:

• A. 0
• B. 20
• C. -20
• D. 40

Answer 1

The correct option is A 0

Since $(x-2)$ is the factor

hence putting $x=2$, we get,

$\Rightarrow 2^3-3(2{)}^2+p(2)+24=0$

$\Rightarrow 8-12+2p+24=0$

$\Rightarrow 2p=-10$

$\Rightarrow (2{)}^2-7(2)+q=0$

$\Rightarrow 4-14+q=0$

$\Rightarrow -10+q=0\Rightarrow q=10$

$\therefore p+q=-10+10=0$