Show that 3x + 2 is a factor of 3x² - x - 2.

Use the Remainder theorem to find which of the following is a factor of 2x³ + 3x² - 5x - 6.

(i) x + 1

(ii) 2x - 1

(iii) x + 2

Find the value of k, if 3x - 4 is a factor of the expression 3x² + 2x - k.

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