1. It is given that: f(x) = 8x3 + 18x2 + 3x -2. a) Use the factor theorem to show that (x + 2) and (4x -1) are factors of f(x). b) Given that the other factor of f(x) is (a + 1 ), find the roots of the equations. (i) f(x) = 0, (ii) f(a) = 0. (Marks available: 5) Answer Answer outline and marking scheme for question: 1 Give yourself marks for mentioning any of the points below: a) Use the factor theorem f (-2) = -64 + 72 - 6 - 2 = 0, thus (x+2) is a factor. f (1/4) = 1/8 + 9/8 + 3/4 - 2 = 0, thus (4x-1) is a factor. (2 marks) b) (i) replacing the given equation with its factors: f (x) = (x+2) (4x-1) (2x+1) This gives roots of x = -2, x = 1/4, x = -1/2. (1 mark) (ii) change the above equation to a function of 2x f (2x) = (2x+2) (8x-1) (4x+1) This gives roots of x = -1, x = 1/8, x = -1/4. (2 marks) (Marks available: 5)