where p(x) = x5 − 4x3 + x2 + 3x + 1, g(x) = x3 − 3x + 1
If the polynomial is divided by another polynomial, the remainder comes out to be, find p and q.
If the polynomial 6x4 + 8x3 − 5x2 + ax + b is exactly divisible by the polynomial 2x2 − 5, the find the values of a and b.
Find the quadratic polynomial, sum of whose zeroes is 8 and their product is 12. Hence, find the zeroes of the polynomial.