Question

If $x-2$ is a factor of $p\left(x\right)=ax-4$, $q\left(x\right)=b{x}^2+3x+9$ and $r\left(x\right)=3x-c$, what is the value of $a+4b+c?$

• A. 12
• B. -12
• C. -13
• D. 13

Answer 1

The correct option is C -13

$\because (x-2)$ is a factor of $p\left(x\right)=ax-4$
$p\left(2\right)=0$
$\Rightarrow 2a-4=0$
$\Rightarrow a=2$

Also,
$\because (x-2)$ is also a factor of $q\left(x\right)=b{x}^2+3x+9$
$q\left(2\right)=0$
$\Rightarrow 4b+12+9=0$
$\Rightarrow 4b=-21$

Also,
$\because (x-2)$ is also a factor of $r\left(x\right)=3x-c$,
$r\left(2\right)=0$
$\Rightarrow 3\left(2\right)-c=0$
$\Rightarrow c=6$

$\therefore a+4b+c=2-21+6=-13$