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

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Find the value of a, if x + 2 is a factor of 4x4 + 2x3 - 3x2 + 8x + 5a.

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Let, f (x) = 4x4 + 2x3 - 3x2 + 8x + 5a

f (-2) = 0

4 (-2)4 + 2 (-2)3 – 3 (-2)2 + 8 (-2) + 5a = 0

64 – 16 – 12 – 16 + 5a = 0

5a = - 20

a = -4

Hence, 

(x + 2) is a factor f (x) when a = -4.

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