Question

Divide the polynomial x⁴ – 5x³ + 5x² + 5x – 6 by each of the following binomials. Write the quotient and remainder.

(3) x – 2

Answer 1

$$\begin{gathered} x^3-3x^2-x+3 \\ x-2\overline{)x^4-5x^3+5x^2+5x-6} \\ {x}^4-2x^3 \\ \underline{-+} \\ 0-3x^3+5x^2 \\ -3x^3+6x^2 \\ \underline{+-} \\ 0-x^2+5x \\ -x^2+2x \\ \underline{+-} \\ 0+3x-6 \\ +3x-6 \\ \underline{-+} \\ 0 \end{gathered}$$

So, the quotient of the division is (x³ – 3x² – x + 3) and the remainder is 0