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. 6
• B. -6
• C. 7
• D. -7

Answer 1

The correct option is D -7

Given, $p\left(x\right)=ax-4$
$q\left(x\right)=b{x}^2+3x+9$
$r\left(x\right)=3x-c$
Now, $x-2$ = 0 $\Rightarrow x=2$
$\therefore$ P(2) = a(2) - 4 = 0
$\Rightarrow 2a=4$
$\Rightarrow a=2$
$q\left(2\right)=b(2{)}^2+3(2)+9=0$
$\Rightarrow 4b+15=0$
$\Rightarrow 4b=-15$
$r\left(2\right)=3\left(2\right)-C=0$
$\therefore a+4b+c=2+(-15)+6=-7$