Final answer:
The given polynomial is classified as 3x³ − 2x² + 5x − 7, which is a polynomial of degree 3, thus the correct option is a.
Step-by-step explanation:
The given polynomial is 3x³ − 2x² + 5x − 7. To classify this polynomial, we need to combine the like terms present in the polynomial. Like terms are the terms which have the same variables and their exponents. As we can see, there are no like terms present in the polynomial, so we can classify the polynomial based on the highest power of variable present in the polynomial. Here, the highest power of the variable is 3, which is present in the first term of the polynomial (3x³). Therefore, the polynomial is classified as 3x³ − 2x² + 5x − 7, which is a polynomial of degree 3.
In a polynomial, the degree of the polynomial is equal to the highest power of the variable present in the polynomial. If there are multiple terms in a polynomial, then the degree of the polynomial is equal to the highest power of the variable present in the polynomial. In the given polynomial, the highest power is 3, which is present in the first term of the polynomial (3x³). Therefore, the degree of the polynomial is 3.
The polynomial can also be classified based on the number of terms present in the polynomial. Here, the polynomial 3x³ − 2x² + 5x − 7 has 4 terms, so this can also be classified as a 4-term polynomial. Thus, we can classify the given polynomial as 3x³ − 2x² + 5x − 7, which is a polynomial of degree 3.