The polynomial Q Q\,Q is defined by Q(x)=x3+3x2+2xQ(x)=x^3+3x^2+2xQ(x)=x3+3x2+2x.
Use the factor theorem to show that (x+1)(x+1)(x+1) and (x+2)(x+2)(x+2) are factors of Q(x)Q(x)Q(x).
Factorise Q(x)Q(x)Q(x) completely.
Hence prove that Q(n)Q(n)Q(n) is divisible by 6 for every integer nnn.
72 exam-style questions on OCR A Level Maths 1.2.10 Manipulating polynomials. Each one has a worked solution and a mark scheme showing where the marks go.