Fill in the blank to correctly complete each sentence. In the term -6x^2y, -6 is the ______.

Verified step by step guidance

1. Identify the components of the term \(-6x^2y\).
2. Recognize that \(-6\) is a numerical factor in the term.
3. Understand that in algebra, the numerical factor of a term is called the 'coefficient'.
4. Therefore, \(-6\) is the coefficient of the term \(-6x^2y\).
5. Fill in the blank with 'coefficient' to complete the sentence.

Key Concepts

Coefficient

A coefficient is a numerical factor that multiplies a variable in an algebraic expression. In the term -6x^2y, the coefficient is -6, which indicates the quantity by which the variable terms x^2 and y are scaled. Coefficients can be positive or negative, affecting the overall sign and magnitude of the term.

Algebraic Term

An algebraic term is a single mathematical expression that can consist of numbers, variables, and exponents. In the expression -6x^2y, the entire term represents a product of the coefficient -6 and the variables x^2 and y. Understanding terms is fundamental in algebra as they form the building blocks of more complex expressions and equations.

Variables

Variables are symbols used to represent unknown values in mathematical expressions and equations. In the term -6x^2y, x and y are variables that can take on different values, allowing for the expression to represent a range of quantities. The use of variables is essential in algebra for formulating general rules and solving problems.