f(x) = 3x^3 – x^2 – 20x – 12 (a) Use the factor theorem to show that (3x + 2) is a factor of f(x). [2 marks] (b) Factorise f(x) fully. [3 marks]

(a) Factor theorem hence, use x = -2/3. Sub in : 3(-2/3)³ - (-2/3)² -20 (-2/3) -12 = 0 (b) (3x+2)(ax² + bx+c) = 3x³ – x² – 20x – 12 3ax³ + (3b+2a)x² + (3c+2b)x + 2c = 3x³ – x² – 20x – 12 Therefore, 3a = 3 ----------> a = 1 3b +2a = -1 -----> b = -1 2c = -12 ---------> c = -6factorise: x² - x- 6 = (x+2)(x-3) Fully factorised: 3x³ – x² – 20x – 12 = (3x+2)(x+2)(x-3)