Final answer:
The polynomial -3x^2 + 11x^3 is a cubic binomial, with the cubic term dictating its classification due to the highest exponent being 3.
Step-by-step explanation:
The polynomial -3x^2 + 11x^3 is a cubic polynomial because the highest degree of the variable x is 3. The degree of a polynomial is determined by the highest exponent of the variable in the polynomial. In this case, the term 11x^3 dictates that it is cubic because the exponent is 3. To name this polynomial, we use the term for the highest degree, which is cubic, and since it has two terms, it is called a binomial.
Understanding the power rules, such as when an exponent is applied to a product (as in xPx9 = x(p+q)), helps in working with polynomials. When dealing with quadratic equations or higher degree polynomials like this one, you can also use graphing tools or other algebraic techniques to understand their behavior. For example, equation graphers can visually display the shape of polynomial curves, which change as the coefficients of the terms are varied.