Question

Show that p – 1 is a factor of p10 + p8 + p6 – p4 – p2 – 1.

Answer 1

see explanation

Explanation:

If (p - 1) is a factor of f(p) then p(1) = 0

p(1) =
`1^(10)` +
`1^(8)` +
`1^(6)` -
`1^(4)` - 1² - 1 = 1 + 1 + 1 - 1 - 1 - 1 = 0

Then (p - 1) is a factor of the polynomial