When the polynomial $2 x^{3} - a x^{2} + 9 x - 8$ is divided by $x - 3$ the remainder is 28. Find the value of a.

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Solution

According to remainder theorem, when $f (x)$ is divided by $(x - 3)$ ,Remanider $= f (3) = 28$ (given).
$f (x) = 2 x^{3} - a x^{2} + 9 x - 8$
$⟹ f (3) = 2 (3)^{3} - a (3)^{2} + 9 (3) - 8$
$⟹ 28 = 54 - 9 a + 27 - 8$
$⟹ 9 a = 73 - 28 = 45$
$⟹ a = \frac{45}{9} = 5$

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