Question

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

• A. 6
• B. -6
• C. 7
• D. -7

Answer 1

The correct option is D -7

Given,
$p\left(x\right)=ax-4$
$q\left(x\right)=b{x}^2+3x+9$
$r\left(x\right)=3x-c$
By remainder theorem, we get,
$x-2=0$
$\therefore x=2$
Substituting the value of $x$ in $p\left(x\right)$
$p\left(2\right)=a\left(2\right)-4=0$
$\Rightarrow 2a=4$
$\therefore a=2$
Substituting the value of $x$ in $q\left(x\right)$
$q\left(2\right)=b(2{)}^2+3(2)+9=0$
$\Rightarrow 4b+15=0$
$\therefore 4b=-15$
Substituting the value of $x$ in $p\left(x\right)$
$r\left(2\right)=3\left(2\right)-c=0$
$\therefore c=6$
Substituting the values of $a,4b,$ and $c$ in the given equation,
$\Rightarrow a+4b+c=2+(-15)+6$
$\therefore a+4b+c=-7$