Question

Show that x-1 is the factor of x^10-1

Answer 1

let g(x) = x-1

for factor g(x) = 0

x-1 = 0

x=1

p(x) = x^10 -1

p(1) = (1)^10 -1

p(1) = 1-1

p(1) =0

hence this shows that x-1 is a factor of this polynomial