Question: For each expression below, select the category to which the expression belongs. Select all that…

For each expression below, select the category to which the expression belongs. Select all that apply.

\[ 3x^3y^6 + 6y^5 + 6 \]

• none of these
• polynomial
• monomial
• trinomial
• binomial

Solution

The expression given is \(3x^3y^6 + 6y^5 + 6\). 1. Polynomial: A polynomial is an expression consisting of variables and coefficients, involving terms with non-negative integer exponents. The given expression fits this definition. 2. Monomial: A monomial is a polynomial with only one term. The given expression has three terms, so it is not a monomial. 3. Trinomial: A trinomial is a polynomial with exactly three terms. The given expression has three terms, so it is a trinomial. 4. Binomial: A binomial is a polynomial with exactly two terms. The given expression has three terms, so it is not a binomial. Therefore, the categories that apply are polynomial and trinomial.