Answer
No, the sum of two trinomials is not always a trinomial.
Work Step by Step
No, the sum of two trinomials is not always a trinomial. Example is provided below.
(3$x^{2}$+2x-9)-(2$x^{2}$+2x-8)
= 3$x^{x}$-2$x^{2}$+2x-2x-9+8
=$x^{2}$-1