Question

Multiplying a trinomial by a trinomial follows the same steps as multiplying a binomial by a trinomial. Determine the degree and maximum possible number of terms for the product of these trinomials: (x2 + x + 2)(x2 – 2x + 3). Explain how you arrived at your answer.

Answer 1

the degree is the highest exponent present in the product

so if you take one term from the first bracket and one term from the second bracket, and multiply them together, which combination will result in the highest degree result? as a major hint, you should try to maximize the exponents in both choices

for the second part, "maximum possible number of terms". imagine your highest term is x^n
the next highest is x^(n-1), etc. until you get to a constant (x^0). apply this logic to your problem to find the max # of terms there can be