Question

Divide the polynomial by the binomial. Write your answer in the form: Dividend = divisor × quotient + remainder

(8) a³ + a; a + 2

Answer 1

(a³ + 8) ÷ (a + 2) can be shown as:

$$\begin{gathered} a^2-2a+4 \\ a+2\overline{)a^3+8} \\ {a}^3+2a^2 \\ \underline{--} \\ 0-2a^2+8 \\ -2a^2-4a \\ \underline{++} \\ +4a+8 \\ +4a+8 \\ \underline{--} \\ \underline{0} \end{gathered}$$

Dividend = divisor × quotient + remainder
$\therefore a^3+8=(a+2)\left(a^2-2a+4\right)+0$