Final answer:
The polynomial 13x^2 + 3x^3 + x is of the third degree because the highest power of x is 3. The polynomial has three terms, so it could also be called a trinomial; however, the degree is usually more important.
Step-by-step explanation:
The polynomial in question is 13x^2 + 3x^3 + x. To determine its name and degree, we look for the highest power of x in the expression. In this case, the highest power of x is 3, which is found in the term 3x^3. The degree of the polynomial is the highest power of x, so this polynomial is of the third degree. The degree tells us a lot about the polynomial, including the number of possible roots and the general shape of its graph.
Polynomials are also classified by the number of terms they contain. A polynomial with one term is called a monomial, two terms a binomial, three terms a trinomial, and more than three terms are simply called polynomials. Because our given polynomial has three terms, it would be referred to as a trinomial. However, in general, the specific name is not as commonly used as the degree when describing polynomials.