Question

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

Answer 1

Solve for the value of an unknown variable by using the remainder theorem.

Let$p\left(y\right)=a–2y+5y^2$and $g\left(y\right)=y-2$

Find the value of $g\left(y\right)$when $y=2$

$$\begin{gathered} g\left(y\right)=y–2 \\ =2–2 \\ =0 \end{gathered}$$

Now, $p\left(y\right)$ is divided by$g\left(y\right)$ and the remainder is $7$

By the remainder theorem,

$$\begin{gathered} p\left(2\right)=7 \\ a–2\times 2+5\left(2\right)2=7 \\ a–4+20=7 \\ a=7–16 \\ a=–9 \end{gathered}$$

Hence, the required answer is $a=-9$