Using factor theorem, show that g(x) is a factor of p(x), when
$p (x) = 2 x^{3} + 9 x^{2} - 11 x - 30, g (x) = x + 5$

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Solution

$f (x) = 2 x^{3} + 9 x^{2} - 11 x - 30$

By the Factor Theorem, (x + 5) will be a factor of f(x) if f(-5) = 0.

Here, $f (- 5) = 2 (- 5)^{3} + 9 (- 5)^{2} - 11 (- 5) - 30 = - 250 + 225 + 55 - 30 = - 280 + 280 = 0$

Therefore, (x + 5) is a factor of $(2 x^{3} + 9 x^{2} - 11 x - 30)$

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