If $(2 x - 3)$ is a factor of $(16 x^{4} + 8 x^{3} - 8 x^{2} - 2 x - a)$ , then find $a$

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Solution

$f (x) = 16 x^{4} + 8 x^{3} - 8 x^{2} - 2 x - a$
if (2x-3) is a factor then f(1.5)=0
$f (1.5) = 16. (1.5)^{4} + 8 (1.5)^{3} - 8 (1.5)^{2} - 2. (1.5) - a = 81 + 27 - 18 - 3 - a = 87 - a = 0$
a=87

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