Is (x-3)(3x+6) factored out completely?

Also will a trinomial always factor as the product of two binomials.

no, I see a common factor of 3 in the second factor

final result...
3(x-3)(x+2)

second question.
If the factors are to contain rational numbers, then no

e.g. x^2 + 2x + 6
we cannot find two rational numbers which when multiplied will give us 6 and when added will give us 2