Question

Find the remainder when the polynomial f(x) = 4x³ − 12x² + 14x − 3 is divided by (2x − 1).

Answer 1

$\mathrm{Let}p\left(x\right)=4x^3-12x^2+14x-3.$

By the remainder theorem, we know that when p(x) is divided by (2x - 1), the remainder is $p\left(\frac{1}{2}\right)$.
Now,
$$\begin{gathered} p\left(\frac{1}{2}\right)=4\times {\left(\frac{1}{2}\right)}^3-12\times {\left(\frac{1}{2}\right)}^2+14\times \frac{1}{2}-3 \\ =\frac{1}{2}-3+7-3 \\ =\frac{3}{2} \end{gathered}$$