Question

Is (x – 5) a factor of the polynomial x³ – 5x – 30?

Answer 1

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).