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Zeroes of a Polynomial

If the polyno...

Question

If the polynomial $(x^{3} - 3 x^{2} + a x + 18)$ is divided by $(x - 4)$ , the reminder is $58$ . Find the value of a.

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Solution

To find the Remainder we have to put $x - 4 = 0 \Rightarrow x = 4$
as
$4^{3} - 3 * 4^{2} + a * 4 + 18 = 58 \Rightarrow 34 + 4 a = 58 \Rightarrow 4 a = 24 \Rightarrow a = 6$

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