Question

If a $-$ 2y + 5y² is divided by (y $-$ 2) the remainder is 7, then find the value of a.

Answer 1

$$\begin{gathered} \mathrm{Let}p\left(y\right)=a-2y+5y^2 \\ \mathrm{Here},\mathrm{divisor}=y-2 \\ \mathrm{When}y-2=0,\mathrm{we}\mathrm{have}y=2 \\ \mathrm{Putting}y=2\mathrm{in}p\left(y\right),\mathrm{we}\mathrm{get}: \\ \mathrm{Remainder}=p\left(2\right)=a-2\left(2\right)+5{\left(2\right)}^2 \\ =a-4+20 \\ =a+16 \\ \mathrm{Given}:\mathrm{Remainder}=7 \\ \mathrm{Now},a+16=7 \\ \Rightarrow a=7-16 \\ \therefore a=-9 \end{gathered}$$