Only a quadratic trinomial is possible.
"Linear" means that the highest power that the x variable can have in the equation is 1. And "trinomial" means there's three terms in it. So for example:
4x + 5x + 9
The highest power is 1, and there's three terms. It's a linear trinomial, right? Wrong. Because 4x and 5x simplify to 9x (which will give 9x + 9), which makes it a linear binomial.
So essentially, a linear trinomial is an unsimplified version of a linear binomial.