Question

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

(4) x – 3

Answer 1

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

So, the quotient of the division is (x³ – 2x² – x + 2) and the remainder is 0