Question

Find the remainder when $x^3-4x^2+5x-1$ is divided by $2x+1$.

• A. $-\frac{21}{8}$
• B. $\frac{-37}{8}$
• C. $\frac{14}{9}$
• D. $\frac{15}{4}$

Answer 1

The correct option is B $\frac{-37}{8}$

$\text{Given polynomial:}p\left(x\right)=x^3-4x^2+5x-1\text{Divisor is:}2x+1$

$\text{Then,}2x+1=02x=-1x=\frac{-1}{2}$

$\text{By Remainder theorem, remainder}\text{is given by}p(-\frac{1}{2}).$

$p(-\frac{1}{2})={(-\frac{1}{2})}^3-4{(-\frac{1}{2})}^2+5(-\frac{1}{2})-1$

$p(-\frac{1}{2})=-\frac{1}{8}-4\left(\frac{1}{4}\right)-\frac{5}{2}-1$

$p(-\frac{1}{2})=-\frac{1}{8}-1-\frac{5}{2}-1$

$p(-\frac{1}{2})=-\frac{37}{8}$

$\text{The remainder of the given}\text{polynomial is}-\frac{37}{8}.$