Question

When $x^4+x^3-2x^2+x+1$ is divided by $x-1$, the remainder is $2$ and the quotient is .

• A. $x^3+x^2+1$
• B. $x^3+2x^2+1$
• C. $x^3+x^2+x$

Answer 1

The correct option is B $x^3+2x^2+1$

Given
$x^4+x^3-2x^2+x+1$
$=(x–1)\times Quotient+2$

$Quotient=\frac{x^4+x^3-2x^2+x-1}{(x–1)}$​

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

So, $Quotient=x^3+2x^2+1$