In the expansion of (1 + 2x)ⁿ, the coefficient of x⁴ is ten times the coefficient of x². Find the value of the positive integer, n.

Mark scheme

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

1. [M3] n(n-1)(n-2)(n-3)(2⁴) / (4×3×2×1) = 10 × n(n-1)(2²) / (2×1) or better condone omitting the factor of n and/or n-1; must have dealt with factorials
2. M2 if one slip/omission or M1 if two slips/omissions
3. or B1 for n(n-1)(2²) [x²] / 2 seen and B1 for n(n-1)(n-2)(n-3)(2⁴)[x⁴] / 24 seen
4. [A1] n² – 5n – 24 [= 0] oe equivalent must be 3-terms, e.g. n² - 5n = 24
5. [M1] (n+3)(n-8) [= 0] or any valid method of solution for their 3-term quadratic
6. [A1] n = 8 only A0 if -3 also given as a final solution, i.e. not discarded If zero scored, allow SC1 for n = 8 unsupported or without correct method