The rational function
x2+px+q(x−1)(x+2)2\displaystyle \frac{x^2+px+q}{(x-1)(x+2)^2}(x−1)(x+2)2x2+px+q
can be written as
Ax−1+Bx+2+C(x+2)2\displaystyle \frac{A}{x-1}+\frac{B}{x+2}+\frac{C}{(x+2)^2}x−1A+x+2B+(x+2)2C.
Given that A=2A=2A=2 and C=5C=5C=5, find BBB, p p\,p and qqq.
281 exam-style questions on CCEA A Level Maths 3.1 Algebra and functions (A-level only), covering 3.1.1 Algebra and functions (A-level only), 3.1.2 Algebra and functions (A-level only), 3.1.3 Algebra and functions (A-level only), 3.1.4 Algebra and functions (A-level only), 3.1.5 Algebra and functions (A-level only), 3.1.6 Algebra and functions (A-level only), 3.1.7 Algebra and functions (A-level only), 3.1.8 Algebra and functions (A-level only), 3.1.9 Algebra and functions (A-level only), and 3.1 Algebra and functions (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.