If x + 2k is a factor of f(x) = x4

– 4k2x

2 + 2x + 3k + 3, find k?


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1. Answer:

   Given, p(x) = x⁴ – 4k²x² + 2x + 3k + 3

   And, x + 2k is a factor.

   So, p(-2k) = 0

   →→→ Putting -2k in place of x,

   => p(-2k) = (-2k)⁴ – (4 × k² × -2k²) + 2(-2k) + 3k + 3

   => 0 = 16k⁴ – 4k²(4k²) – 4k + 3k + 3

   => 0 = 16k⁴ – 16k⁴ – 4k + 3k + 3

   => 0 = -k + 3… [cancelling 16k⁴ and -16k⁴]

   => k = 3… [shifting k to LHS]

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