Question

$\text{If the dividend =}{x}^4+x^3-2x^2+x+1,\text{divisor =}x-1\text{and remainder =}2,\text{then find the quotient q(x)}.$

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

Answer 1

The correct option is C

$x^3+2x^2+1$

$\text{Given:}\text{Dividend =}{x}^4+x^3-2x^2+x+1,$$\text{divisor =}x-1\text{and remainder =}2$
$\text{To find: Quotient}q\left(x\right)$


$$\begin{array}{c}{x}^3+2x^2+1\\ x-1x^4+x^3-2x^2+x-1\\ \underset{–}{-x^4+x^3}2\\ 2x^3-2x^2+x-1\\ \underset{–}{-2x^3+2x^2}\\ 0x^2+x-1\\ \underset{–}{-x+1}\\ 0\end{array}$$$\text{Hence, the quotient is}{x}^3+2x^2+1.$