Question

Please give the solution.

Answer 1

p-1 = 0

then, p = 1

putting the value of p in both factors

(p)10 - 1

as p = 1

(1)10 - 1

1 - 1

0

now

(p)11 - 1 = (1)11 -1 = 1 - 1 = 0

Answer 2

Let f(x) = p^10 - 1.

f(1) = (1)^10 - 1

    = 1 - 1

    = 0.

By factor theorem, p - 1 is a factor of p^10 - 1.

Let g(x) = p^11 - 1.

f(1) = 1^11 - 1

    = 1 - 1

   = 0.

By factor theorem, p - 1 is a factor of p^11 - 1.

Therefore, (p - 1) is a factor of (p)^10 - 1 and (p)^11 - 1.

Hope this helps!