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.
40 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.