The cubic polynomial 6x3+kx2+25x−126x^3 + kx^2 + 25x - 126x3+kx2+25x−12 is denoted by f(x)f(x)f(x). It is given that (2x+3)(2x + 3)(2x+3) is a factor of f(x)f(x)f(x).
Use the factor theorem to show that k=31k = 31k=31.
Using this value of kkk, factorise f(x)f(x)f(x) completely.
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.
