Questions: For each expression below, select the category to which the expression belongs. Select all that apply. 4 x polynomial binomial trinomial monomial none of these 4 x^3 + 6 y^3 binomial trinomial monomial polynomial none of these

Solution Steps

To categorize the given expressions, we need to understand the definitions:

1. Monomial: An expression with only one term.
2. Binomial: An expression with exactly two terms.
3. Trinomial: An expression with exactly three terms.
4. Polynomial: An expression with one or more terms, where each term is a product of a constant and a variable raised to a non-negative integer power.

Given the expressions:

1. \(4x\)
2. \(4x^3 + 6y^3\)

1. For \(4x\):

   • It has only one term, so it is a monomial.
   • Since it has one or more terms, it is also a polynomial.

2. For \(4x^3 + 6y^3\):

   • It has exactly two terms, so it is a binomial.
   • Since it has one or more terms, it is also a polynomial.

The expression \(4x\) has only one term. According to the definitions:

• A monomial is an expression with only one term.
• A polynomial is an expression with one or more terms.

Thus, \(4x\) is both a monomial and a polynomial.

The expression \(4x^3 + 6y^3\) has exactly two terms. According to the definitions:

• A binomial is an expression with exactly two terms.
• A polynomial is an expression with one or more terms.

Thus, \(4x^3 + 6y^3\) is both a binomial and a polynomial.

Final Answer