O-LevelAdditional MathematicsFactors of polynomials4037/22 · May/June 2017 · Q35 Marks

Without using a calculator, factorise the expression 10x³ – 21x² + 4.

Mark scheme

Marking points from the official mark scheme (May/June 2017). The mark or mark type is shown in brackets.

[B1] Correctly finding a correct linear factor or root from a valid method, e.g. factor theorem used or long division or synthetic division: f(2)=10(2³)-21(2²)+4 = 0
[B1] correct linear factor stated or implied by, e.g. (x-2)(10x²-x-2)
[B2] Correct quadratic factor (10x²-x-2) or (5x²-8x-4) or (2x²-5x+2) found using any valid method; [B1] for any 2 terms correct
[B1] (x-2)(2x-1)(5x+2) mark final answer
[B1] for correctly finding a correct linear factor or root
[B1] for a correct linear factor stated or implied
[SC3] for the full, complete and correct working to find the remaining two linear factors and arrive at the correct product of 3 linear factors

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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 2017 Paper 2 Variant 2, question 3.

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