The polynomial `x^(6)+4x^(5)+3x^(4)+2x^(3)+x+1` is divisible by: (where `omega` is one of the imaginary cube roots of unity)

The polynomial x^(6)+4x^(5)+3x^(4)+2x^(3)+x+1 is divisible by ( where w is the cube root of units )/(x+omega b.)x+omega^(2) c.(x+omega)(x+omega^(2)) d.(x-omega)(x-omega^(2)) where omega is one of the imaginary cube roots of unity.

If the polynomial x^(3)+6x^(2)+4x+k is divisible by x+2 then value of k is

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

The common roots of the equation x^(3) + 2x^(2) + 2x + 1 = 0 and 1+ x^(2008)+ x^(2003) = 0 are (where omega is a complex cube root of unity)

For the polynomial p(x)=x^(5)+4x^(3)-5x^(2)+x-1 , one of the factors is

The value of the determinant |(1,omega^(3),omega^(5)),(omega^(3),1,omega^(4)),(omega^(5),omega^(4),1)| , where omega is an imaginary cube root of unity, is

The number of imaginary roots of x^(6)2x^(5)+7x+4=0 is

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