Question

(y² $-$ 11y + 30) $÷$ (y $-$ 5)

Answer 1

$$\begin{gathered} \mathrm{Dividend}=y^2-11y+30 \\ \mathrm{Index}\mathrm{form}=y^2-11y+30 \\ \mathrm{Coefficient}\mathrm{form}=\left(1,-11,30\right) \\ \mathrm{Comparing}\mathrm{the}\mathrm{divisor}y-5\mathrm{with}y-a,\mathrm{we}\mathrm{get}a=5 \end{gathered}$$



$$\begin{gathered} \mathrm{Now},\mathrm{quotient}\mathrm{in}\mathrm{coefficient}\mathrm{form}=\left(1,-6\right) \\ \therefore \mathrm{Quotient}=y-6\mathrm{in}\mathrm{the}\mathrm{variable}y \\ \mathrm{Remainder}=0 \\ \therefore y^2-11y+30=\left(y-5\right)\left(y-6\right)+0 \end{gathered}$$