Problem 22 - Beginning and Intermediate Algebra

Question

In each term, give the numerical coefficient. \(9 n^{6}\)

Step-by-Step Solution

Answer

The numerical coefficient is 9.

Step 1: Identify the Coefficient

In any algebraic expression, the coefficient is the numerical part that multiplies the variable. In this case, the term is given as \(9 n^{6}\).

Step 2: Extract the Coefficient

Ignore the variable part \(n^{6}\) and look only at the number in front of it. This number is the numerical coefficient.

Step 3: Conclusion

The numerical coefficient of the term \(9 n^{6}\) is \(9\).

Key Concepts

Numerical Coefficient

A numerical coefficient is the number part of an algebraic term that multiplies the variable. It's important to recognize and separate this value when working with algebraic expressions. For example, in the term \(9n^6\), the numerical coefficient is \(9\). This means that \(9\) is the factor that multiplies the variable part, which in this case is \(n^6\). Identifying the numerical coefficient can help in simplifying and solving algebraic expressions effectively.

Variables in Algebra

Variables in algebra are symbols used to represent numbers in expressions and equations. They are usually denoted by letters, such as \(x\), \(y\), or \(n\). Variables are placeholders for values that can change or vary. For instance, in the term \(9n^6\), \(n\) is the variable. This means that \(n\) can take different numerical values. Variables are crucial in algebra because they allow us to generalize mathematical concepts and solve problems involving unknown quantities.

Algebraic Terms

An algebraic term is a combination of numbers and variables connected by multiplication. Each term consists of a numerical coefficient and a variable part. For example, in the term \(9n^6\), \(9\) is the numerical coefficient and \(n^6\) is the variable part. Algebraic terms are the building blocks of algebraic expressions. An expression can have one or multiple terms. Understanding the components of an algebraic term is essential when performing operations such as addition, subtraction, multiplication, and division in algebra.