Question Determine if the expression \( -\frac{7}{m^{3}} \) is a polynomial or not. If it is a polynomial, state the type and degree of the polynomial. Answer Attempt 1 out of 2 The given expression Submit Answer

To determine whether the expression \( -\frac{7}{m^{3}} \) is a polynomial, let's review the definition of a polynomial: **Definition of a Polynomial:** A polynomial in one variable \( m \) is an expression of the form: \[ a_n m^n + a_{n-1} m^{n-1} + \dots + a_1 m + a_0 \] where: - \( a_n, a_{n-1}, \dots, a_0 \) are constants (coefficients). - \( n \) is a non-negative integer representing the degree of the polynomial. **Analyzing the Given Expression:** \[ -\frac{7}{m^{3}} \] This can be rewritten using negative exponents: \[ -7m^{-3} \] **Key Points:** 1. **Exponents:** In a polynomial, the exponents of the variable must be non-negative integers (0, 1, 2, 3, ...). Here, the exponent is \(-3\), which is negative. 2. **Form:** The presence of a negative exponent indicates that the variable is in the denominator, which violates the polynomial definition. **Conclusion:** Since the expression \( -\frac{7}{m^{3}} \) involves a negative exponent, it **does not** qualify as a polynomial. **Final Answer:** The expression \( -\frac{7}{m^{3}} \) is **not** a polynomial because it includes a negative exponent.