trinomial algebra

Question

How do you do this and how do solve it?Use the  button to create a trinomial that has the following end behavior:

Answer 1

A trinomial (polynomial with three terms) with that sort of behavior (falling to the left and falling to the right) would be one of even degree with the leading coefficient negative.

An example of a trinomial with even degree and leading coefficient negative would be -x**3 + x + 5, the degree being the sum of the exponents (3 + 1 = 4) and the coefficient of the leading term being -1.