Let remainder when $p (x)$ is divided by $q (x)$ using remainder theorem is $A$ . $p (x) = x^{9} - 5 x^{4} + 1, q (x) = x + 1$
Find the value of $A + 10$ .

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Solution

$p (x) = x^{9} - 5 x^{4} + 1$ and
$g (x) = x + 1$
$=> x + 1 = 0$
$=> x = - 1$
The remainder when $p (x)$ is divided by $g (x)$ is $p (- 1)$ (By Remainder Theorem)
Thus,
$p (- 1) = (- 1)^{9} - 5 (- 1)^{4} + 1$
$= - 1 - 5 + 1$
$= - 5$

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