Find the remainder when : $p (x) = 3 x^{3} - 4 x^{2} + 7 x + 5$ is divided by $(x - 3)$ and $(x + 3)$

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Solution

$p (x) = 3 x^{3} - 4 x^{2} + 7 x + 5$
According to remainder theorm, $p (3) a n d p (- 3)$ will give us the remainder
$p (3) = 3 (3)^{3} - 4 (3)^{2} + 7 (3) + 5$
$= 81 - 36 + 21 + 5 = 71$

$p (- 3) = 3 (- 3)^{3} - 4 (- 3)^{2} + 7 (- 3) + 5$
$= - 81 - 36 - 21 + 5 = - 133$

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