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Question
Find the value of a, if x + 2 is a factor of 4x4 + 2x3 − 3x2 + 8x + 5a.
Solution
Let 4x4 + 2x3 − 3x2 + 8x + 5a be the polynomial.
By the factor theorem,
(x+2)is a factor of f(x) if f(−2) = 0.
Therefore,
`f(2) = 4(-2)^4 + 2(-2)^3 - 3(-2)^2 + 8(-2) + 5a = 0`
`64 - 16 - 12 - 16 + 5a = 0`
`5a = -20`
`a = -4`
Hence, `a = -4`
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