Question

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

(3) 5a – 12 + 3a² – 5a³ + 6a⁴ ÷ a² – 1

Answer 1

( 6a⁴ – 5a³ + 3a² + 5a – 12) ÷ ( a² – 1) can be shown as:

$$\begin{gathered} 6a^2-5a+9 \\ {a}^2-1\overline{)6a^4-5a^3+3a^2+5a-12} \\ -\underline{+6a^4+0-6a^2} \\ -5a^3+9a^2+5a \\ \underline{+-5a^3+0+5a} \\ 9a^2-12 \\ \underline{-9a^2-9} \\ \underline{0-3} \end{gathered}$$

Dividend = divisor × quotient + remainder
$\therefore 6a^4-5a^3+3a^2+5a-12=(a^2-1)\left(6a^2-5a+9\right)-3$