Using the remainder theorem, factorise each of the following completely :

3x³ + 2x² - 23x - 30

Using the remainder theorem, factorise each of the following completely :

4x³ + 7x² - 36x - 63

Using the Remainder Theorem, factorise the expression 3x³ + 10x² + x - 6. Hence, solve the equation 3x³ + 10x² + x - 6 = 0.

Factorise the expression

f(x) = 2x³ - 7x² - 3x + 18.

Hence, find all possible values of x for which f(x) = 0.