Question

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

(7) x³ – 6x² + 11x – 6; x – 3

Answer 1

(x³ – 6x² + 11x – 6) ÷ (x – 3) can be shown as:

$$\begin{gathered} x^2-3x+2 \\ x-3\overline{)x^3-6x^2+11x-6} \\ {x}^3-3x^2 \\ \underline{-+} \\ 0-3x^2+11x \\ -3x^2+9x \\ \underline{+-} \\ 2x-6 \\ 2x-6 \\ \underline{-+} \\ \underline{0} \end{gathered}$$

Dividend = divisor × quotient + remainder
$\therefore x^3-6x^2+11x-6=(x-3)\left(x^2-3x+2\right)+0$