f(x)=x3+8x2+px+qf(x) = x^3 + 8x^2 + px + qf(x)=x3+8x2+px+q
Given that f(3)=0f(3) = 0f(3)=0 and f(−5)=16f(-5) = 16f(−5)=16
Find the values of p p\,p and q q\,q and 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.