f(x)=x3+9x2+px+qf(x) = x^3 + 9x^2 + px + qf(x)=x3+9x2+px+q
Given that f(2)=0f(2) = 0f(2)=0 and f(−5)=14f(-5) = 14f(−5)=14
Find the values of p p\,p and qqq
Factorise f(x)f(x)f(x) completely.
257 exam-style questions on Edexcel A Level Maths Algebraic Methods, covering 7.1 Algebraic Fractions, 7.2 Dividing Polynomials, 7.3 The Factor Theorem, 7.4 Mathematical Proof, and 7.5 Methods of Proof. Each one has a worked solution and a mark scheme showing where the marks go.