Question

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

(1) x + 1

Answer 1

$$\begin{gathered} x^3-6x^2+11x-6 \\ x+1\overline{)x^4-5x^3+5x^2+5x-6} \\ {x}^4+x^3 \\ \underline{--} \\ 0-6x^3+5x^2 \\ -6x^3-6x^2 \\ \underline{++} \\ 0+11x^2+5x \\ 11x^2+11x \\ \underline{--} \\ 0-6x-6 \\ -6x-6 \\ \underline{++} \\ 0 \end{gathered}$$
So, the quotient of the division is (x³ – 6x² + 11x – 6) and the remainder is 0