A company's weekly profit PPP, in thousands of pounds, is modeled by the polynomial P(n)=5n3+kn2+8n−30P(n) = 5n^3 + kn^2 + 8n - 30P(n)=5n3+kn2+8n−30, where n n\,n is the number of units sold (in hundreds) and k k\,k is a constant. A financial analysis reveals that when P(n)P(n)P(n) is divided by (n−2)(n - 2)(n−2), the remainder is 2. Find the value of kkk.
368 exam-style questions on Edexcel A Level Maths Algebraic Methods, covering 1.1 Proof by Contradiction, 1.2 Algebraic Fractions, 1.3 Partial Fractions, 1.4 Repeated Factors, and 1.5 Algebraic Division. Each one has a worked solution and a mark scheme showing where the marks go.