Is x (4x2 + 8x + 12) completely factored? If not, what other factoring can occur?
No, the expression x(4x^2 + 8x + 12) is not completely factored. The binomial 4x^2 + 8x + 12 can still be factored further. It is a quadratic trinomial, and it can be factored as follows:
4x^2 + 8x + 12 = 4(x^2 + 2x + 3)
Using the quadratic formula or by completing the square, the quadratic trinomial x^2 + 2x + 3 cannot be factored further over the rational numbers.