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

User IntegerWolf
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1 Answer

13 votes
13 votes

Answer:

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

User Wouter Verlaek
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3.0k points