Show that the polynomial `x^(4p)+x^(4q+1)+x^(4r+2)+x^(4s+3)` is divisible by `x^3+x^2+x+1, w h e r ep ,q ,r ,s in ndot`

Prove that x^(3p) + x^(3q+1) + x^(3r+2) is exactly divisible by x^2+x+1 , if p,q,r is integer.

Prove that x^(3p) + x^(3q+1) + x^(3r+2) is exactly divisible by x^2+x+1 , if p,q,r is integer.

Let P(x) and Q(x) be two polynomials. If f(x) = P(x^4) + xQ(x^4) is divisible by x^2 + 1 , then

Find the number of polynomials of the form x^3+a x^2+b x+c that are divisible by x^2+1,w h e r ea , b ,c in {1,2,3,9,10}dot

The polynomial px^(3)+4x^(2)-3x+q completely divisible by x^2-1: find the values of p and q. Also for these values of p and q factorize the given polynomial completely.

Let P(x) and Q(x) be two polynomials.Suppose that f(x) = P(x^3) + x Q(x^3) is divisible by x^2 + x+1, then (a) P(x) is divisible by (x-1),but Q(x) is not divisible by x -1 (b) Q(x) is divisible by (x-1), but P(x) is not divisible by x-1 (c) Both P(x) and Q(x) are divisible by x-1 (d) f(x) is divisible by x-1

Find the values of p\ a n d\ q so that x^4+p x^3+2x^2-3x+q is divisible by (x^2-1)

For which values of a and b , the zeroes of q(x) = x^(3)+2x^(2)+a are also the zeroes of the polynomial p(x) = x^(5)-x^(4)-4x^(3)+3x^(2)+3x +b ? Which zeores of p(x) are not the zeroes of q(x) ?

If zeros of the polynomial f(x)=x^3-3p x^2+q x-r are in A.P., then (a) 2p^3=p q-r (b) 2p^3=p q+r (c) p^3=p q-r (d) None of these