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.

Solve (x-1)^(n)=x^(n), where n is a positive integer.

Show that there will be no term containing x^(2r) in the expansion of (x+x^-2)^(n-3) if n-2r is a positive integer but not a multiple of 3.

If n is an odd positve integer greater than 3 then (n^(3)-n^(2))-3(n^(2)-n) is always a multiple of

int(x-a)(x^(n-1)+x^(n-2)a+...+a^(n-1))dx where n is +ve integer =

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

Use factor theorem to prove that (x+a) is a factor of (x^(n)+a^(n)) for any odd positive integer n .

Use factor theorem to verify that x+a is a factor of x^(n)+a^(n) for any odd positive integer.

If n is n odd integer that is greater than or equal to 3 but not a multiple of 3, then prove that (x+1)^(n)=x^(n)-1 is divisible by x^(3)+x^(2)+x

(x+1) is a factor of x^(n)+1 only if n is an odd integer (b) n is an even integer n is a negative integer (d) n is a positive integer