Given that (x+4)(x + 4)(x+4) and (x−3)(x - 3)(x−3) are both factors of f(x)f(x)f(x), where
f(x)=px3−3x2−42x+q f(x) = px^3 - 3x^2 - 42x + q f(x)=px3−3x2−42x+qFind the values of p p\,p and qqq.
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.