Question

If $r\left(x\right)=6x^2+7x-2$ and $t\left(x\right)=2x^2+7x-1$, then which of the following functions is divisible by $2x+5$?

• A. $p\left(x\right)=r\left(x\right)+t\left(x\right)$
• B. $p\left(x\right)=2r\left(x\right)+t\left(x\right)$
• C. $p\left(x\right)=r\left(x\right)+3t\left(x\right)$
• D. $p\left(x\right)=2r\left(x\right)+3t\left(x\right)$

Answer 1

Answer: (C)

$p\left(x\right)=r\left(x\right)+3t\left(x\right)$

$p\left(x\right)=r\left(x\right)+3t\left(x\right)$ is the function divisible by $2x+5$
$r\left(x\right)+3t\left(x\right)=6x^2+7x-2+6x^2+21x-3$
$=12x^2+28x-5$
When $x=\frac{-5}{2}$
$=12{\left(\frac{-5}{2}\right)}^2+28\left(\frac{-5}{2}\right)-5$
$=75-70-5$
$=0$