Question

If dividend = $x^4+x^3-2x^2+x+1$, divisor = x - 1 and remainder = 2. Find the quotient q(x).

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

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

$$\begin{array}{c}{x}^3+2x^2+1\\ x-1x^4+x^3-2x^2+x-1\\ \underset{–}{x^4-x^3}2\\ 2x^3-2x^2+x-1\\ \underset{–}{2x^3-2x^2}\\ x-1\\ \underset{–}{x-1}\\ 0\end{array}$$

$\therefore q\left(x\right)=x^3+2x^2+1$.