Show that `(x-1)` is a factor of `x ^(n)-1.`

Show that (x-1) is a factor of x ^(10) -1 and also of x ^(11) -1.

Using factor theorem, show that (x-5) is a factor of the polynomial 2x^(3) - 5x^(2) - 28x + 15

Determine whether (x-1) is a factor of the following polynomials : x^(4) + 5x^(2) - 5x +1

Show that (x-2) , (x+3) and (x-4) are factors of x ^(3) -3x ^(2) -10x + 24.

Show that (x +4) ,(x-3) and (x-7) are factors of x ^(3) - 6x ^(2) - 19 x + 84.

Prove that x^3 + x^2 + x is factor of (x+1)^n - x^n -1 where n is odd integer greater than 3, but not a multiple of 3.

If both (x-2) and ( x- (1)/(2)) are the factors of ax^(2) + 5x + b , then show that a =b .