Identify the coefficient and the degree of each term of the pols \( 31 x^{2} y^{7}-5 x^{3} y z-1 \) The degree of \( 31 x^{2} y^{7} \) is 9 The degree of \( -5 x^{3} y z \) is 5 The coefficient of -1 is -1 The degree of -1 is 0 The degree of the polynomial is

To identify the coefficient and the degree of each term in the polynomial \( 31 x^{2} y^{7} - 5 x^{3} y z - 1 \), let's break it down term by term. 1. **First term: \( 31 x^{2} y^{7} \)** - Coefficient: \( 31 \) - Degree: The degree is the sum of the exponents of the variables. Here, \( 2 + 7 = 9 \). 2. **Second term: \( -5 x^{3} y z \)** - Coefficient: \( -5 \) - Degree: The degree is the sum of the exponents of the variables. Here, \( 3 + 1 + 1 = 5 \). 3. **Third term: \( -1 \)** - Coefficient: \( -1 \) - Degree: The degree of a constant term is \( 0 \). Now, let's summarize the findings: - For \( 31 x^{2} y^{7} \): - Coefficient: \( 31 \) - Degree: \( 9 \) - For \( -5 x^{3} y z \): - Coefficient: \( -5 \) - Degree: \( 5 \) - For \( -1 \): - Coefficient: \( -1 \) - Degree: \( 0 \) The degree of the polynomial is the highest degree among its terms. In this case, the highest degree is \( 9 \) from the term \( 31 x^{2} y^{7} \). Thus, the degree of the polynomial is **9**.