Question

(y³ + 343) $÷$ (y + 7)

Answer 1

$$\begin{gathered} \mathrm{Dividend}=y^3+343 \\ \mathrm{Index}\mathrm{form}=y^3+0y^2+0y+343 \\ \mathrm{Coefficient}\mathrm{form}=\left(1,0,0,343\right) \\ \mathrm{Comparing}\mathrm{the}\mathrm{divisor}y+7\mathrm{with}y-a,\mathrm{we}\mathrm{get}a=-7 \end{gathered}$$



$$\begin{gathered} \mathrm{Now},\mathrm{quotient}\mathrm{in}\mathrm{coefficient}\mathrm{form}=\left(1,-7,49\right) \\ \therefore \mathrm{Quotient}=y^2-7y+49\mathrm{in}\mathrm{the}\mathrm{variable}y \\ \mathrm{Remainder}=0 \\ \therefore y^3+343=\left(y+7\right)\left(y^2-7y+49\right)+0 \end{gathered}$$