Step 1 :Given the difference between two trinomials is $5x^2 + 11x - 16$. One of the trinomials is $3x^2 - 2x + 7$. Let the other trinomial be $ax^2 + bx + c$.
Step 2 :Set up the equation: $(ax^2 + bx + c) - (3x^2 - 2x + 7) = 5x^2 + 11x - 16$
Step 3 :Simplify the equation: $(a - 3)x^2 + (b + 2)x + (c - 7) = 5x^2 + 11x - 16$
Step 4 :Equate the coefficients of the corresponding terms:
Step 5 :$a - 3 = 5$
Step 6 :$b + 2 = 11$
Step 7 :$c - 7 = -16$
Step 8 :Solve for $a$, $b$, and $c$: $a = 8$, $b = 9$, $c = -9$
Step 9 :\(\boxed{8x^2 + 9x - 9}\) is the other trinomial.