The coefficient of x7 in the expansion of (px²+4/x)5 is 1280. Find the value of the constant p.

Mark scheme

Marking points from the official mark scheme (May/June 2025). The mark or mark type is shown in brackets.

1. [1] B1 May be seen in a list. Allow with or without x's. Condone missing brackets only if recovered later. (5 choose 3) or (5 choose 2) or 10x(px^2)^(5-3)x(4/x)^3
2. [1] B1 This term must now be identified if given as part of a list. Allow with or without x's. 10p^2x^64/p^3
3. [1] M1 Condone e.g. 640x^7/p = 1280 if x^7 then disappears in subsequent work. Must be from a x (px^2)^3 x (4/x)^2
4. [1] A1 OE SC B1 for (5 choose 4) or (5 choose 1) or 5x(px^2)^5-1 x (4/x)^1 => p=4. p=1/2