quadrants formed by the asymptotes. (5 marks) Correctly shows that either M1 f(3) = 0, = 0 or = 0 f(−2) Draws the conclusion that (x 3), (x + 2) or (2x + 1) must therefore be a factor. M1 – Either makes an attempt at long division by setting up the long division, or makes an attempt to M1 find the remaining factors by matching coefficients. For example, stating or or For the long division, correctly finds the the first two coefficients. A1 For the matching coefficients method, correctly deduces that = 2 and = 2 or correctly deduces that = 2 and = or correctly deduces that = 1 and a c r q u w −3 = –6 For the long division, correctly completes all steps in the division. A1 For the matching coefficients method, correctly deduces that = 5 or correctly deduces that = or correctly deduces that = b p v −5 –1 States a fully correct, fully factorised final answer: A1 (x 3)(2x + 1)(x + 2) – (6 marks) NOTES: Other algebraic methods can be used to factorise h(x). For example, if (x 3) is known to be a factor then – by balancing (M1) by factorising (M1) by factorising (A1)
quadrants formed by the asymptotes. (5 marks) Correctly shows that either f(3) = 0, f(−2) = 0 or = 0 M1 Draws the conclusion that (x – 3), (x + 2) or (2x + 1) must therefore be a factor. M1 Either makes an attempt at long division by setting up the long division, or makes an attempt to find the remaining factors by matching coefficients. For example, stating or or M1 For the long division, correctly finds the the first two coefficients. For the matching coefficients method, correctly deduces that a = 2 and c = 2 or correctly deduces that r = 2 and q = −3 or correctly deduces that u = 1 and w = –6 A1 For the long division, correctly completes all steps in the division. For the matching coefficients method, correctly deduces that b = 5 or correctly deduces that p = −5 or correctly deduces that v = –1 A1 States a fully correct, fully factorised final answer: (x – 3)(2x + 1)(x + 2) A1 (6 marks) NOTES: Other algebraic methods can be used to factorise h(x). For example, if (x – 3) is known to be a factor then by balancing (M1) by factorising (M1) by factorising (A1)