Use remainder theorem to find the value of k, it being given that when x³ + 2x² + kx + 3 is divided by (x – 3), then the remainder is 21.

Show that the polynomial f(x) = x⁴ + 4x² + 6 has no zero.

If one zero of the polynomial p(x) = x³ – 6x² + 11x – 6 is 3, find the other two zeros.

If two zeros of the polynomial p(x) = 2x⁴ – 3x³ – 3x² + 6x – 2 are √2 and – √2, find its other two zeros.

Find the quotient when p(X) = 3x⁴ + 5x³ – 7x² + 2x + 2 is divided by (x² + 3x + 1)