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Question
Is (x – 5) a factor of the polynomial x3 – 5x – 30?
Solution
Let f(x) = x2 – 5x – 30.
By factor theorem, (x – 5) will be the factor of f(x), if f(v) = 0.
Now, f(v) = (5)3 – 5(v) – 30
= 125 – 25 – 30
= 70
∵ f(v) ≠ 0
Hence, (x – 5) is not a factor of f(x).
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