To classify the expressions 5x, 3x4, 7x3, and 10, we first need to look at them in two ways: by the number of terms and by degree.
Classification by Number of Terms
1. 5x – This expression has one term, so it is classified as a monomial.
2. 3x4 – This expression also has one term, making it a monomial as well.
3. 7x3 – Like the previous two, it has one term, thus it’s another monomial.
4. 10 – This number is a constant and can also be considered a monomial, since it has no variable component.
In summary, all four terms (5x, 3x4, 7x3, and 10) are classified as monomials.
Classification by Degree
The degree of a monomial is determined by the highest exponent of the variable in the term.
1. 5x – The degree is 1 (since the exponent of x is 1).
2. 3x4 – The degree is 4.
3. 7x3 – The degree is 3.
4. 10 – Since this is a constant, it is considered to have a degree of 0.
To summarize the classification by degree: 5x is degree 1, 3x4 is degree 4, 7x3 is degree 3, and 10 is degree 0.