Question

If dividend = $x^4+x^3-2x^2+x+1$ and divisor = $(x-1)$, find the quotient, $q\left(x\right)$ and remainder $r\left(x\right)$.

• A. q(x) = $x^3+2x^2+x+1$ and r(x) = -1
• B. q(x) = -$x^3+x^2+x$ and r(x) = 4
• C. q(x) = $x^3+2x^2+1$ and r(x) = 2
• D. q(x) = $x^3+2x^2+1$ and r(x) = 0

Answer 1

The correct option is C

q(x) = $x^3+2x^2+1$ and r(x) = 2

Given, $x^4+x^3-2x^2+x+1$ = $(x-1)q\left(x\right)+r\left(x\right)$

$$\begin{array}{c}{x}^3+2x^2+1\\ x-1x^4+x^3-2x^2+x+1\\ \underset{–}{x^4-x^3}\\ 2x^3-2x^2+x+1\\ \underset{–}{2x^3-2x^2}\\ x+1\\ \underset{–}{x-1}\\ 2\end{array}$$