A-LevelMathematicsAlgebra9709/23 · May/June 2017 · Q67 Marks

Use the factor theorem to show that (x + 2) is a factor of the expression 6x³ + 13x² - 33x – 70 and hence factorise the expression completely.

(i)Use the factor theorem to show that (x + 2) is a factor of the expression 6x³ + 13x² - 33x – 70 and hence factorise the expression completely.[5]
(ii)Deduce the roots of the equation 6 + 13y - 33y² – 70y³ = 0.[2]

Mark scheme

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

[M1] Evaluate expression when x = −2
[A1] Obtain 0 with all necessary detail present Use of f(x) = (x + 2)(ax² + bx + c) to find a, b and c, allow M1 A0 Use of f(x) = (x+2)(ax² +bx+c)+d to find a, b and c, and show d = 0, allow M1 A1
[M1] Carry out division, or equivalent, at least as far as x² and x terms in quotient
[A1] Obtain 6x²+x-35
[A1] Obtain factorised expression (x+2)(2x+5)(3x-7)
[M1] State or imply substitution x = 1/y or equivalent
[A1] Obtain -1/2, -2/5, 3/7

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Topic: Algebra, A-Level Mathematics (syllabus 9709). Structured question, 7 marks.
Source: A-Level Mathematics, May/June 2017 Paper 2 Variant 3, question 6.

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