Question

If $x-2$ is a factor of both $p\left(x\right)=3x-a$ and $q\left(x\right)=4x-b,$ what is the value of $a+b?$

• A. 6
• B. 8
• C. 14
• D. 13

Answer 1

The correct option is C 14

$\because x-2isafactorofp\left(x\right)andq\left(x\right)$, we can say
$p\left(2\right)=0andq\left(2\right)=0$.

$\therefore p\left(2\right)=0$
$\Rightarrow$ $3\left(2\right)-a=0$
$\Rightarrow$ $a=6$

Also,
$q\left(2\right)=0$
$\Rightarrow$ $4\left(2\right)-b=0$
$\Rightarrow$ $b=8$

$\therefore a+b=6+8=14$