In Which Expression Is The Coefficient Of The $n$ Term -1?A. 3 N 2 + 4 N − 1 3n^2 + 4n - 1 3 N 2 + 4 N − 1 B. 4 N 2 + N − 5 4n^2 + N - 5 4 N 2 + N − 5 C. − 2 N 2 − N + 5 -2n^2 - N + 5 − 2 N 2 − N + 5 D. − N 2 + 5 N + 4 -n^2 + 5n + 4 − N 2 + 5 N + 4

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**In which expression is the coefficient of the $n$ term -1?**

Understanding the Coefficient of a Term

In algebra, the coefficient of a term is the numerical value that multiplies the variable. For example, in the expression $3n^2 + 4n - 1$, the coefficient of the $n^2$ term is 3, the coefficient of the $n$ term is 4, and the coefficient of the constant term is -1.

Analyzing the Options

To determine which expression has a coefficient of -1 for the $n$ term, we need to examine each option carefully.

Option A: 3n2+4n−13n^2 + 4n - 1

In this expression, the coefficient of the $n^2$ term is 3, the coefficient of the $n$ term is 4, and the coefficient of the constant term is -1. However, the coefficient of the $n$ term is 4, not -1.

Option B: 4n2+n−54n^2 + n - 5

In this expression, the coefficient of the $n^2$ term is 4, the coefficient of the $n$ term is 1, and the coefficient of the constant term is -5. Again, the coefficient of the $n$ term is 1, not -1.

Option C: −2n2−n+5-2n^2 - n + 5

In this expression, the coefficient of the $n^2$ term is -2, the coefficient of the $n$ term is -1, and the coefficient of the constant term is 5. Here, the coefficient of the $n$ term is indeed -1.

Option D: −n2+5n+4-n^2 + 5n + 4

In this expression, the coefficient of the $n^2$ term is -1, the coefficient of the $n$ term is 5, and the coefficient of the constant term is 4. However, the coefficient of the $n$ term is 5, not -1.

Conclusion

Based on our analysis, the correct answer is Option C: −2n2−n+5-2n^2 - n + 5, as it is the only expression where the coefficient of the $n$ term is -1.

Frequently Asked Questions

Q: What is the coefficient of a term in an algebraic expression?

A: The coefficient of a term is the numerical value that multiplies the variable.

Q: How do I determine the coefficient of a term in an expression?

A: To determine the coefficient of a term, look for the numerical value that multiplies the variable. For example, in the expression $3n^2 + 4n - 1$, the coefficient of the $n^2$ term is 3, the coefficient of the $n$ term is 4, and the coefficient of the constant term is -1.

Q: What is the difference between the coefficient and the exponent of a term?

A: The coefficient is the numerical value that multiplies the variable, while the exponent is the power to which the variable is raised. For example, in the expression $3n^2$, the coefficient is 3 and the exponent is 2.

Q: Can the coefficient of a term be a fraction or a decimal?

A: Yes, the coefficient of a term can be a fraction or a decimal. For example, in the expression $\frac{1}{2}n^2 + 4n - 1$, the coefficient of the $n^2$ term is $\frac{1}{2}$, the coefficient of the $n$ term is 4, and the coefficient of the constant term is -1.

Q: How do I identify the coefficient of the constant term in an expression?

A: The constant term is the term that does not have a variable. To identify the coefficient of the constant term, look for the numerical value that is not multiplied by a variable. For example, in the expression $3n^2 + 4n - 1$, the coefficient of the constant term is -1.