Find $P$ if $a^{3} - 2 a^{2} + p a + 4 = - 5$ for $a = - 2$ .

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Solution

Given that for $a = - 2$
$a^{3} - 2 a^{2} + p a + 4 = - 5$
${(- 2)}^{3} - 2 (4) + p (- 2) + 4 = - 5$
$- 8 - 8 - 2 p + 4 = - 5$
$- 16 + 4 + 5 = 2 p$
$2 p = - 16 + 9$
$2 p = - 7$
$p = - \frac{7}{2}$

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