Question

find the remainder when p(x)=4x³-12x²+14x-3 we when divided by x-½

Answer 1

By the remainder theorem, when f(x) is divided by x-a, the remainder is f(a).
$x - \frac{1}{2} = 0 \\ x = \frac{ 1 }{2}$
Substituting x's value in the given equation :
$4 {x}^{3} - 12 {x}^{2} + 14x - 3 \\ =4 \times {( \frac{1}{2}) }^{3} - 12 \times { (\frac{1}{2}) }^{2} + 14 \times \frac{1}{2} - 3 \\ = \frac{4}{8} - \frac{12}{4} + \frac{14}{2} - 3 \\ = \frac{1}{2} - 3 + 7 - 3 \\ = 1 \frac{1}{2}$

Answer 2

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