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O-LevelAdditional MathematicsFactors of polynomials4037/22 · Oct/Nov 2015 · Q15 Marks

It is given that f(x) = 4x³ – 4x² – 15x + 18.

(i)Show that x + 2 is a factor of f(x).[1]
(ii)Hence factorise f(x) completely and solve the equation f(x) = 0.[4]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2015). The mark or mark type is shown in brackets.

[B1] (i) f(-2)=-32-16+30+18=0 All four evaluated terms must be seen. Allow if correct long division used
[M1] (ii) f(x) = (x + 2)(4x² −12x+9) Coefficients 4 and 9
[A1] (ii) Coefficient -12
[A1] (ii) = (x + 2)(2x – 3)(2x-3) All three factors together
[A1] (ii) f(x) = 0 → x = −2, 1.5 nfww Allow 1.5 mentioned just once

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About this question

Topic: Factors of polynomials, O-Level Additional Mathematics (syllabus 4037). Structured question, 5 marks.
Source: O-Level Additional Mathematics, Oct/Nov 2015 Paper 2 Variant 2, question 1.

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