Using factor theorem, show that:

(3 - 2x) is a factor of (2x³ - 9x² + x + 12).

Use factor theorem to show that (x + 2) and (2x - 3) are factors of (2x² + x - 6).

For what value of a is the polynomial (2x³ + ax² + 11x + a + 3) exactly divisible by (2x - 1)?

What must be subtracted from the polynomial x³ + x² - 2x + 1, so that the result is exactly divisible by (x - 3)?