Find the value of 'a', if $x + 2$ is a factor of $4 x^{4} + 2 x^{3} - 3 x^{2} + 8 x + 5 a$ .

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Solution

$∵$ x + 2 is a factor of $4 x^{4} + 2 x^{3} - 3 x^{2} + 8 x + 5 a$

$∴$ Remainder will be 0.

Now dividing $4 x^{4} + 2 x^{3} - 3 x^{2} + 8 x + 5 a b y x + 2$ , we get

Remainder = 5a + 20

$∴$ 5a + 20 = 0

$\Rightarrow 5 a = - 20$

$\Rightarrow a = \frac{- 20}{5}$

$\Rightarrow a = - 4$

$∴ a = - 4$

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