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`

Show that the polynomial x^(4p)+x^(4q+1)+x^(4r+2)+x^(4s+3) is divisible by x^(3)+x^(2)+x+1, where p,q,r,s in n

For what value of a is the polynomial p(x)=2x^(4)-ax^(3)+4x^(2)+2x+1 is divisible by 1-2x

If the polynomial x^(6)+px^(5) +qx^(4) -x^(2)-x-3 is divisible by (x^(4) -1) , then the value of p^(2)+q^(2) is

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

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

If the polynomial 8x^(4)+14x^(3)-2x^(2)+px+q is exactly divisible by 4x^(2)+3x-2 , then the values of p and q respectively are

Find the values of p and q so that x^(4)+px^(3)+2x^(2)-3x+q is divisible by (x^(2)-1)

Let polynomial P(x)=x^(5)+2x^(4)-x^(3)+2x^(2)+3 ,is divided by polynomial D(x)=x^(2)-x+2 then we get remainder "R(x)" and quotient "Q(x)" such that P(x)=Q(x)*D(x)+R(x) then : (A) Q(x)=x^(3)+3x^(2)-4x, (B) Q(x)=x^(3)+3x^(2)-4 (C) R(x)=-4x+11, (D) R(x)=4x+11

The HCF of the polynomials 9(x +a)^(p) (x -b)^(q) (x + c)^(r) and 12(x + a)^(p +3) (x -b)^(q-3) (x +c)^(r +2) " is " 3(x +a)^(6) (x -b)^(6) (x + c)^(6) , then the value of p +q -r is