Question

Use synthetic division method for performing the following divisions. Write the result in the form
Divident = Divisor $\times$ Quotient + Remainder.

(i) (x³ $-$ 4x² $-$ 2x + 1) $÷$ (x $-$ 3)

Answer 1

$$\begin{gathered} \mathrm{Dividend}=x^3-4x^2-2x+1 \\ \mathrm{Index}\mathrm{form}=x^3-4x^2-2x+1 \\ \mathrm{Coefficient}\mathrm{form}=\left(1,-4,-2,1\right) \\ \mathrm{Comparing}\mathrm{the}\mathrm{divisor}x-3\mathrm{with}x-a,\mathrm{we}\mathrm{get}a=3 \end{gathered}$$



$$\begin{gathered} \mathrm{Now},\mathrm{quotient}\mathrm{in}\mathrm{coefficient}\mathrm{form}\mathrm{is}\left(1,-1,-5\right) \\ \therefore \mathrm{Quotient}=x^2-x-5\mathrm{in}\mathrm{the}\mathrm{variable}x \\ \mathrm{Remainder}=-14 \\ \therefore x^3-4x^2-2x+1=\left(x-3\right)\left(x^2-x-5\right)-14 \end{gathered}$$