Question

The remainder when $4a^3-12a^2+14a-3$ is divided by $2a-1$, is

• A. $\frac{2}{3}$
• B. $\frac{5}{3}$
• C. $\frac{6}{7}$
• D. $\frac{3}{2}$

Answer 1

The correct option is D $\frac{3}{2}$

Given that:

$P\left(x\right)=4a^3-12a^2+14a-3$

Since if we divide by $2a-1$ than, by division algorithm we can say there exists $Q\left(x\right)\&R\left(x\right)$ such that:

$P\left(x\right)=(2a-1)Q\left(x\right)+R\left(x\right)$

We have to find $R\left(x\right)$

So,

$4a^3-12a^2+14a-3=(2a-1)(2a^2-5a+\frac{9}{2})+\frac{3}{2}$

So,

$R\left(x\right)=\frac{3}{2}$

So remainder is $\frac{3}{2}$