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Question
Determine whether (x – 1) is a factor of the following polynomials:
x3 + 5x2 – 10x + 4
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Solution
Let P(x) = x3 + 5x2 – 10x + 4
By factor theorem (x – 1) is a factor of P(x), if P(1) = 0
P(1) = 13 + 5(12) – 10(1) + 4 = 1 + 5 – 10 + 4
P(1) = 0
∴ (x – 1) is a factor of x3 + 5x2 – 10x + 4
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