To classify the expression [tex]\(5x + 3x^2 - 7x^3 + 2\)[/tex], let's analyze its structure and the degrees of the terms.
1. Identify the degrees of each term:
- [tex]\(5x\)[/tex]: The degree of this term is 1 (since [tex]\(x\)[/tex] is raised to the power of 1).
- [tex]\(3x^2\)[/tex]: The degree of this term is 2 (since [tex]\(x\)[/tex] is raised to the power of 2).
- [tex]\(-7x^3\)[/tex]: The degree of this term is 3 (since [tex]\(x\)[/tex] is raised to the power of 3).
- [tex]\(2\)[/tex]: This is a constant term with a degree of 0 (since there is no [tex]\(x\)[/tex]).
2. Determine the highest degree:
- Out of the four terms, [tex]\(-7x^3\)[/tex] has the highest degree, which is 3.
3. Classify the polynomial based on the highest degree:
- Polynomials are classified by their highest degree term.
- If the highest degree is 1, it is a linear expression.
- If the highest degree is 2, it is a quadratic expression.
- If the highest degree is 3, it is a cubic expression.
- If the highest degree is 4, it is a quartic expression.
Given that the highest degree in the expression [tex]\(5x + 3x^2 - 7x^3 + 2\)[/tex] is 3, we classify this expression as a cubic expression.
Therefore, the correct classification of the expression [tex]\(5x + 3x^2 - 7x^3 + 2\)[/tex] is:
- Cubic expression.
