To classify the expression [tex]\(5x^3 + 2x - 3\)[/tex], we need to identify the degree of the polynomial. Let's break it down step-by-step:
1. Identify the terms in the polynomial: The given expression is [tex]\(5x^3 + 2x - 3\)[/tex]. This polynomial has three terms:
- [tex]\(5x^3\)[/tex]
- [tex]\(2x\)[/tex]
- [tex]\(-3\)[/tex]
2. Determine the degree of each term:
- The term [tex]\(5x^3\)[/tex] has a degree of 3 (since the exponent of [tex]\(x\)[/tex] is 3).
- The term [tex]\(2x\)[/tex] has a degree of 1 (since the exponent of [tex]\(x\)[/tex] is 1).
- The constant term [tex]\(-3\)[/tex] has a degree of 0 (since there is no [tex]\(x\)[/tex] term).
3. Find the degree of the polynomial: The degree of the polynomial is the highest degree of its terms. In this case, the term with the highest degree is [tex]\(5x^3\)[/tex], which has a degree of 3.
4. Classify the expression based on its degree:
- A polynomial of degree 1 is called a Linear expression.
- A polynomial of degree 2 is called a Quadratic expression.
- A polynomial of degree 3 is called a Cubic expression.
- Polynomials of higher degrees or expressions involving variable exponents (e.g., [tex]\(a^x\)[/tex]) fall into other categories, such as Exponential expressions.
Since the degree of the polynomial [tex]\(5x^3 + 2x - 3\)[/tex] is 3, we classify it as a Cubic expression.
Therefore, the correct classification for the expression [tex]\(5x^3 + 2x - 3\)[/tex] is:
Cubic expression.
