To determine how many variable terms are in the expression [tex]\(3x^3 y + 5xz - 4y + x - z + 9\)[/tex], we need to identify each term and its variables. Let's break down the expression term by term:
1. First term: [tex]\(3x^3 y\)[/tex]
- This term includes the variables [tex]\(x\)[/tex] (raised to the third power) and [tex]\(y\)[/tex].
2. Second term: [tex]\(5xz\)[/tex]
- This term includes the variables [tex]\(x\)[/tex] and [tex]\(z\)[/tex].
3. Third term: [tex]\(-4y\)[/tex]
- This term includes the variable [tex]\(y\)[/tex].
4. Fourth term: [tex]\(x\)[/tex]
- This term includes the variable [tex]\(x\)[/tex].
5. Fifth term: [tex]\(-z\)[/tex]
- This term includes the variable [tex]\(z\)[/tex].
6. Sixth term: [tex]\(9\)[/tex]
- This term is a constant and does not include any variables.
Now, we count the terms that include variables:
- [tex]\(3x^3 y\)[/tex]
- [tex]\(5xz\)[/tex]
- [tex]\(-4y\)[/tex]
- [tex]\(x\)[/tex]
- [tex]\(-z\)[/tex]
There are 5 terms with variables.
Thus, the number of variable terms in the expression is:
[tex]\[
5
\][/tex]
