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