Question

When p(x) = 4x³ − 12x² + 11x − 5 is divided by (2x − 1), the remainder is
(a) 0
(b) −5
(c) −2
(d) 2

Answer 1

(c) −2

$2x-1=0\Rightarrow x=\frac{1}{2}$
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, we have:
$$\begin{gathered} p\left(\frac{1}{2}\right)=4\times {\left(\frac{1}{2}\right)}^3-12\times {\left(\frac{1}{2}\right)}^2+11\times \frac{1}{2}-5 \\ =\frac{1}{2}-3+\frac{11}{2}-5 \\ =-2 \end{gathered}$$