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Question
Use the factor theorem to determine that x - 1 is a factor of x6 - x5 + x4 - x3 + x2 - x + 1.
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Solution
Let f(x) = x6 - x5 + x4 - x3 + x2 - x + 1 to check whether x - 1 is a factor of x6 - x5 + x4 - x3 + x2 - x + 1 we find f(1).
Put x = 1 in equation (i) we get
f(1) = (1)6 - (1)5 + (1)4 - (1)3 + (1)2 - (1) + 1
= 1 - 1 + 1 - 1 + 1 - 1 + 1
= 4 - 3
= 1.
Since, f(1) ≠ 0, So by factor theorem (x - 1) is not a factor of f(x).
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