When $p (x) = 4 x^{3} - 12 x^{2} + 11 x - 5$ is divided by (2x-1), the remainder is
(a) 0
(b) -5
(c) -2
(d) 2

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Solution

ANSWER:
(c) −2
$2 x - 1 = 0 \Rightarrow x = \frac{1}{2}$
By the remainder theorem, we know that when p(x) is divided by (2 x - 1), the remainder is $p (\frac{1}{2}$ .
Now, we have:
$p (\frac{1}{2}) = 4 \times (\frac{1}{2})^{3} - 12 \times (\frac{1}{2})^{2} + 11 \times \frac{1}{2} - 5$
= $\frac{1}{2} - 3 + \frac{11}{2} - 5 = - 2$

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