It is given that f(x)=x3+6x2+px+qf(x) = x^3 + 6x^2 + px + qf(x)=x3+6x2+px+q where p p\,p and q q\,q are constants.
It is also given that f(4)=0f(4) = 0f(4)=0 and f(−5)=36f(-5) = 36f(−5)=36.
Find the values of p p\,p and qqq.
Factorise f(x)f(x)f(x) completely.
132 exam-style questions on OCR (MEI) A Level Maths 1.1 Proof, covering 1.1.1 Structure of mathematical proof, 1.1.2 Disproof by counter example, 1.1.3 Proof by contradiction (A-level only), and 1.1 Proof. Each one has a worked solution and a mark scheme showing where the marks go.