Let's break down the algebraic expression [tex]\(5x + 8y - 12z\)[/tex] to identify the components asked in the question:
1. Understanding an algebraic expression:
An algebraic expression is composed of variables, coefficients, terms, and operations.
2. Variables:
Variables are symbols that represent unknown values. In the expression [tex]\(5x + 8y - 12z\)[/tex], the variables are [tex]\(x\)[/tex], [tex]\(y\)[/tex], and [tex]\(z\)[/tex].
3. Operations:
Operations are mathematical processes like addition, subtraction, multiplication, and division. In the expression [tex]\(5x + 8y - 12z\)[/tex], the operations are addition ([tex]\(+\)[/tex]) and subtraction ([tex]\(-\)[/tex]).
4. Terms:
Terms are parts of the algebraic expression that are separated by addition or subtraction. In the expression [tex]\(5x + 8y - 12z\)[/tex], the terms are [tex]\(5x\)[/tex], [tex]\(8y\)[/tex], and [tex]\(-12z\)[/tex].
5. Coefficients:
Coefficients are the numerical factors that are multiplied by the variables in an algebraic term. In the expression [tex]\(5x + 8y - 12z\)[/tex], the coefficients are the numbers that multiply the variables:
- In the term [tex]\(5x\)[/tex], the coefficient is 5.
- In the term [tex]\(8y\)[/tex], the coefficient is 8.
- In the term [tex]\(-12z\)[/tex], the coefficient is [tex]\(-12\)[/tex].
Therefore, the values 5, 8, and -12 are coefficients.
