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Question
Determine whether (x – 1) is a factor of the following polynomials:
x4 + 5x2 – 5x + 1
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Solution
Let P(x) = x4 + 5x2 – 5x + 1
By factor theorem, (x – 1) is a factor of P(x), if P(1) = 0
P(1) = 14 + 5 (12) – 5(1) + 1
= 1 + 5 – 5 + 1
= 2 ≠ 0
∴ (x – 1) is not a factor of x4 + 5x2 – 5x + 1
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