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`

Divide the polynomial 2x ^(4) - 4x ^(3) - 3x -1 by (x-1)

In the polynomial g(x)= x-2, q(x)= x^(2)-x+1 and r(x)= 4 find p(x)

The degree of polynomial p (x) = x^2 – 3x + 4x^3 - 6 is

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

When Polynomial (2x^(3)+ax^(2)+3x-5) and (x^(3)+x^(2)-4x-a) are divisible by x-1 leaves the same remainder find the value of a.

The HCF of polynomials (x^(2) - 4x +4) (x+3) and (x^(2) + 2x-3)(x-2) is ______

Using Division Algorithm prove that the polynomial g(x) = x^(2) + 3x + 1 is a factor of f(x) = 3 x^(4) + 5 x^(3) - 7 x^(2) + 2x + 2

Differentiate the following w.r.t.x. (x^(2)+x+1)^(4)

What must be added to the polynomial P(x)= x^(4)+2x^(3)-2x^(2)+x-1 So that the resulting polynomial is excatly divisible by x^(2)+x-3

Statement -1 If the equation (4p-3)x^(2)+(4q-3)x+r=0 is satisfied by x=a,x=b nad x=c (where a,b,c are distinct) then p=q=3/4 and r=0 Statement -2 If the quadratic equation ax^(2)+bx+c=0 has three distinct roots, then a, b and c are must be zero.