A quantitative analyst models the projected value of a high-risk portfolio using the function V(x)=(4+kx)7V(x) = (4 + kx)^7V(x)=(4+kx)7, where xxx represents market volatility and kkk is a positive sensitivity constant.
Find the first three terms, in ascending powers of xxx, in the expansion of (4+kx)7(4 + kx)^7(4+kx)7 giving each term in its simplest form.
Given that the coefficient of x2x^2x2 is exactly three-eighths of the coefficient of xxx, determine the value of kkk.
Practise Edexcel A Level Maths Binomial Expansion with exam-style questions for A Level Maths. 100 questions covering 4.1 Expanding (1 + x)^n, 4.2 Expanding (a + bx)^n, and 4.3 Using Partial Fractions, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.