Question

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

(6) 4n – 4n² + 4n+ n⁵ – n⁴ ; n³ – 4

Answer 1

( n⁵ – n⁴ – 4n² + 4n ) ÷ (n³ – 4) can be shown as:

$$\begin{gathered} n^2-n \\ {n}^3-4\overline{)n^5-n^4-4n^2+4n} \\ {n}^5+0-4n^2 \\ \underline{-+} \\ 0-n^4+0+4n \\ -n^4+0+4n \\ \underline{+-} \\ \underline{0+0} \end{gathered}$$

Dividend = divisor × quotient + remainder
$\therefore n^5-n^4-4n^2+4n=(n^3-4)\left(n^2-n\right)+0$