Divide the polynomial p(x) = x⁴ – 5x + 6 by g(x) = 2 – x² and find the quotient and remainder.

Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial:

P(x) = x³ – 3x + 1 and q(x) = x⁵ – 4x³ + x² + 3x + 1

On dividing x³ – 3x² + x + 2 by a polynomial g(x), the quotient and remainder were (x – 2) and (–2x + 4) respectively. Find g(x).

Find the condition that the zeros of the polynomial f(x) = x³ + 3px² + 3qx + r may be in A.P.