If 2x + 1 is a factor of 2x² + ax - 3, find the value of a.

Find the values of constants a and b when x - 2 and x + 3 both are the factors of expression x³ + ax² + bx - 12.

Find the values of m and n so that x - 1 and x + 2 both are factors of

x³ + (3m + 1)x² + nx - 18.

When x³ + 2x² - kx + 4 is divided by x - 2, the remainder is k. Find the value of constant k.