To determine the number of variable terms in the expression [tex]\( 3x^3y + 5x^2 - 4y + z + 9 \)[/tex], let's break it down step by step:
1. Identify and separate the terms in the expression:
- [tex]\(3x^3y\)[/tex]
- [tex]\(5x^2\)[/tex]
- [tex]\(-4y\)[/tex]
- [tex]\(z\)[/tex]
- [tex]\(9\)[/tex]
2. Determine which of these terms are variable terms:
- A variable term is a term that includes at least one variable (such as [tex]\(x\)[/tex], [tex]\(y\)[/tex], or [tex]\(z\)[/tex]).
- [tex]\(3x^3y\)[/tex] includes variables [tex]\(x\)[/tex] and [tex]\(y\)[/tex]
- [tex]\(5x^2\)[/tex] includes variable [tex]\(x\)[/tex]
- [tex]\(-4y\)[/tex] includes variable [tex]\(y\)[/tex]
- [tex]\(z\)[/tex] includes variable [tex]\(z\)[/tex]
- [tex]\(9\)[/tex] is a constant term and does not include any variables
3. Count the number of variable terms:
- [tex]\(3x^3y\)[/tex]
- [tex]\(5x^2\)[/tex]
- [tex]\(-4y\)[/tex]
- [tex]\(z\)[/tex]
There are 4 variable terms in the expression.
Therefore, the number of variable terms in the expression [tex]\( 3x^3y + 5x^2 - 4y + z + 9 \)[/tex] is:
Blank 1: [tex]\(\boxed{4}\)[/tex]
