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

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

4x + 1 is a factor of ____

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

Factors of 12 x ^(2) + 11 x +2

Show that the sum of the coefficients of x^(25) and x^(-10) of (x^(4) -(1)/(x^(3)))^(15) is zero.

Show that x + (1)/(x) is increasing on [1, oo) .

Show that Lt_(x to 0)(log(1+x))/(x^(2))=1

Show that (x)/(1+x) lt ln (1+x) lt x AA x gt 0 .

Use the Factor Theorem to determine whether g(x) is factor of f(x) in each of the following cases : f(x)=5x^(3)+x^(2)-5x-1,g(x)=x+1