Question

6. Show that x -1 is a factor of x5 -1 while x5 +1 is not divisible by x -1.

Answer 1

Answer:

By factor theorem,

(i)  f(1) should be = 0 if x - 1 is a factor of f(x).      (f(x) = x⁵ - 1)

f(1) = 1⁵ - 1 = 0

(ii)  f(1) for x⁵ + 1 = 1⁵ + 1 = 2

Hence x + 1 is not a factor of x⁵ + 1

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