Classifying mathematical expressions involves understanding two key concepts: the number of terms in each expression and the degree of those terms.
1. Classification by Number of Terms: An expression can be classified into three categories based on its number of terms:
- Monomial: An expression with a single term.
Example: 5x (one term). - Binomial: An expression with two terms.
No examples here as all given expressions have more or less than two terms. - Trinomial: An expression with three terms.
No examples here either as there are no expressions with exactly three terms.
Let’s evaluate each expression:
- 5x: This is a monomial because it has one term.
- 3x^4: Also a monomial with one term.
- 7x^3: Again a monomial with one term.
- 10: This is a monomial (constant term) with one term.
Thus, all four expressions can be classified as monomials.
2. Classification by Degree: The degree of a term is the highest power of the variable in the term.
- 5x: The degree is 1 (since the power of x is 1).
- 3x^4: The degree is 4 (the highest power of x is 4).
- 7x^3: The degree is 3 (the highest power of x is 3).
- 10: The degree is 0, since it is a constant and does not contain a variable.
In summary:
- All expressions (5x, 3x^4, 7x^3, and 10) are classified as monomials.
- Degrees are: 5x (degree 1), 3x^4 (degree 4), 7x^3 (degree 3), and 10 (degree 0).
This classification helps in understanding the structure and nature of each expression for further mathematical operations.