O-LevelAdditional MathematicsFactors of polynomials4037/22 · May/June 2016 · Q45 Marks

Do not use a calculator in this question. The polynomial p(x) = 2x³ – 3x² + qx + 56 has a factor x – 2.

(i)Show that q = -30.[1]
(ii)Factorise p(x) completely and hence state all the solutions of p(x) = 0 .[4]

Mark scheme

Marking points from the official mark scheme (May/June 2016). The mark or mark type is shown in brackets.

[B1] 2(2)³ -3(2)² + 2q + 56 = 0 with one correct interim step leading to q = -30 NB = 0 must be seen or may be implied by e.g. -60 = 2q or 60 = -2q; or convincingly showing 2(2)³ -3(2)² - 30(2)+56 = 0; allow for only 16-12+2(-30) + 56 = 0 or correct synthetic division at least as far as 2 | 2 -3 q 56 | 4 2 2q+4 | 2 1 q+2 0 then q = -30
[B2] 2x²+x-28 B1 for any two terms correct
[M1] For factorising the correct equation; condone = 0; condone (2x - 7)(x + 4) only for M1 but for A1 must see all 3 factors in this part; do not allow (x - 7/2)
[A1] x = 2, x = -4, x = 3.5 oe not from wrong working; answers only do not score

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Topic: Factors of polynomials, O-Level Additional Mathematics (syllabus 4037). Structured question, 5 marks.
Source: O-Level Additional Mathematics, May/June 2016 Paper 2 Variant 2, question 4.

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