Question

Using remainder theorem, find the remainder when:
(4x³ − 12x² + 11x − 5) is divided by (2x − 1)

Answer 1

We have:
$2x-1=0\Rightarrow x=\frac{1}{2}$
By the remainder theorem, we know that when f(x) is divided by (2x $-$ 1), the remainder is f($\frac{1}{2}$).
Thus, we have:
$$\begin{gathered} f\left(x\right)=\left(4x^3-12x^2+11x-5\right) \\ \therefore f\left(\frac{1}{2}\right)=\left[4\times {\left(\frac{1}{2}\right)}^3-12\times {\left(\frac{1}{2}\right)}^2+11\times \left(\frac{1}{2}\right)-5\right] \\ =\left(\frac{1}{2}-3+\frac{11}{2}-5\right) \\ =-2 \end{gathered}$$

Hence, the required remainder is $-$2.