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x2 + 2x + k is a factor of 2x4 + x3 - 14x2 + 5x + 6. Find the value of k.

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We get the remainder as (21 + 7k)x + 2k2 + 8k + 6.

Since x2 + 2x + k is a factor of the given polynomial, the remainder should be zero.

Hence,

21 + 7k = 0 and 2k2 + 8k + 6 = 0 at the same time.

k = -3 satisfies both equations.

Hence k = -3.

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