f(x)=4x3−8x2−35x+75f(x) = 4x^3 - 8x^2 - 35x + 75f(x)=4x3−8x2−35x+75
Use the factor theorem to show that (x+3)(x + 3)(x+3) is a factor of f(x)f(x)f(x).
Hence, show that f(x)f(x)f(x) can be written in the form f(x)=(x+3)(ax+b)2f(x) = (x + 3)(ax + b)^2f(x)=(x+3)(ax+b)2, where a a\,a and b b\,b are integers to be found.
Practise Edexcel A Level Maths Algebraic Methods with exam-style questions for A Level Maths. 261 questions covering 7.1 Algebraic Fractions, 7.2 Dividing Polynomials, 7.3 The Factor Theorem, 7.4 Mathematical Proof, and 7.5 Methods of Proof, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
