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

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Solution

$We have to find the value of a if (x + 2) is a factor of (4 x^{4} + 2 x^{3} - 3 x^{2} + 8 x + 5 a) . S ubstituting x = - 2 in 4 x^{4} + 2 x^{3} - 3 x^{2} + 8 x + 5 a, we get : 4 (- 2)^{4} + 2 (- 2)^{3} - 3 (- 2)^{2} + 8 (- 2) + 5 a = 0 or, 64 - 16 - 12 - 16 + 5 a = 0 or, 5 a = - 20 or, a = - 4 ∴ If (x + 2) is a factor of (4 x^{4} + 2 x^{3} - 3 x^{2} + 8 x + 5 a), a = - 4 .$

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