Given (x+3)(x + 3)(x+3) and (x−5)(x - 5)(x−5) are both factors of f(x)f(x)f(x), where
f(x)=px3−7x2−kx+q f(x) = px^3 - 7x^2 - kx + q f(x)=px3−7x2−kx+qFind the values of p p\,p and q q\,q in terms of kkk.
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.