Is the sum of two trinomials always a trinomial? Explain why or why not. Give an example.

Answer 1

Not always. Here is an example.

f(x) = x³ + x² + 1

g(x) = 2x³ - x² + 9

Both are trinomials. Now add them and get

f(x) + g(x) = (1 + 2)x³ + (1 - 1)x² + (1 + 9) = 3x³ + 10

The result is a binomial.