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.

Determine whether n is an add or even positive integer, when (x + 1) is a factor of (x^(n)-1) .

Show that if n be odd, x + 1 is a factor of x^n + 1 .

If (x - 1) is a factor of the polynomial f(x), but not a factor of the polynomial g(x), then (x - 1) is a factor of which one of the followings ?

It is given that n is an odd integer greater than 3 but n is not multiple of 3. prove that (x^(3)+x^(2)+x) is a factor of (1+x)^(n)-x^(n)-1 .

It is given that n is an odd integer greater than 3 but n is not a multiple of 3 prove that x^3+x^2+x is a factor of (x+1)^n-x^n-1:

Determine whether (x + 1) is a factor of the follwing polynomials or not : 4x^(3)+x^(2)+4x+1 .

Determine whether (x + 1) is a factor of the follwing polynomials or not : x^(3)+x^(2)+x+1

Show that 2.6.10.14.. To n factors =(n+1)(n+2)(n+3) … to n factors.

Show that the coefficients of x^(m) and x^(n) are equal to the expansion of (1+x)^(m+n) .