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)`

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

Find the values of p and q, so that f(x) = {(x^(2) + 3x + p,x le 1),(qx + 2,x gt 1):} is differentiable at x=1.

Prove that p + q = 0 " if " x^(3) - 3px + 2q " is divisible by" (x + 1)^(2)

Find the values of p and q , so that f(x)={{:(x^(2)+3x+p, ifxle1),(qx+2,ifx gt1):} is differentiable at x = 1

Find the values of p and q , so that f(x)={{:(x^(2)+3x+p, ifxle1),(qx+2,ifx gt1):} is differentiable at x = 1

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

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 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.

Find the values of a and b for which zeros of q(x) = x^(3) + 2x^(2) +a are also the zero of p(x) = x^(5) - x^(4) - 4x^(3) + 3x^(2) + 3x +bp . Also, find zeros of p(x) which are not zeros of q(x) .

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