Question

If p-1 is a factor of p^4 +p^2 +p-k, the value of k is what?

Answer 1

k = 3

Explanation:

Since p - 1 is a factor then p(1) = 0

p(x) =
`p^(4)` + p² + p - k, thus

p(1) =
`1^(4)` + 1² + 1 - k = 0, that is

1 + 1 + 1 - k = 0

3 - k = 0 ⇒ k = 3