The remainder, when $x^3-4x^2+5x-1$ is divided by $2x+1$ is

A) $-\frac{21}{8}$

B) $\frac{22}{7}$

C) $\frac{14}{9}$

D) $\frac{15}{4}$

The correct option is B: $\frac{22}{7}$
According to remainder theorem, If a polynomial $p\left(x\right)$ is divided by a binomial $(x-a)$ then the remainder obtained is $p\left(a\right).$
so, $2x+1=0$
$x=-\frac{1}{2}$
so, $p(-\frac{1}{2}$) will be the remainder.
Let $p\left(x\right)=x^3-4x^2+5x-1$
Put $x=-\frac{1}{2}$ in the above polynomial $p\left(x\right)$
$p\left(\frac{-1}{2}\right)={(-\frac{1}{2})}^3-4{(-\frac{1}{2})}^2+5(-\frac{1}{2})-1$
$=-\frac{1}{8}-4\left(\frac{1}{4}\right)-\frac{5}{2}-1$
$=-\frac{1}{8}-\frac{5}{2}-2$
$=\frac{-1-20-16}{8}$
$=-\frac{37}{8}$
Therefore, the remainder is $-\frac{37}{8}$.