Bartlett Moreno
07/22/2023 · High School
Identify the coefficient and the degree of ea \( 31 x^{2} y^{7}-5 x^{3} y z-1 \) The coefficient of \( 31 x^{2} y^{7} \) is 31 The degree of \( 31 x^{2} y^{7} \) is 9 The coefficient of \( -5 x^{3} y z \) is
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To identify the coefficient and the degree of the term \(-5 x^{3} y z\):
1. **Coefficient**: The coefficient of the term \(-5 x^{3} y z\) is \(-5\).
2. **Degree**: The degree of a term is the sum of the exponents of all the variables in that term. In \(-5 x^{3} y z\):
- The exponent of \(x\) is \(3\).
- The exponent of \(y\) is \(1\) (since \(y\) is the same as \(y^1\)).
- The exponent of \(z\) is \(1\) (since \(z\) is the same as \(z^1\)).
Therefore, the degree is:
\[
3 + 1 + 1 = 5
\]
So, the coefficient of \(-5 x^{3} y z\) is \(-5\) and the degree is \(5\).
Quick Answer
The coefficient of \(-5 x^{3} y z\) is \(-5\) and the degree is \(5\).
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