Question

If $a-2y+5y^2$ is divided by $(y-2)$ the reminder is $7$, then find value of $a$.

• A. $a=-3$
• B. $a=-6$
• C. $a=-9$
• D. none of the above

Answer 1

The correct option is C $a=-9$

Let,
$p\left(y\right)=a-2y+5y^2$
$g\left(y\right)=y-2$
$\Rightarrow y-2=0$
$\Rightarrow y=2$
Given,$p\left(y\right)$ is divided by $g\left(y\right)$ and remainder is $7$
Thus, by remainder Theorem,
$p\left(2\right)=7$
$\Rightarrow a-2\left(2\right)+5(2{)}^2=7$
$\Rightarrow a-4+20=7$
$\Rightarrow a=7-16$
$\Rightarrow a=-9$