To determine the number of variable terms in the expression 3x³y + 5x² + 4y + z + 9, we first need to identify what constitutes a variable term.
A variable term is a term that includes at least one variable, as opposed to a constant term, which contains only numerical values. In our expression, the components can be broken down as follows:
- 3x³y: This term has two variables, x and y.
- 5x²: This term contains one variable, x.
- 4y: This term has one variable, y.
- z: This is a variable term by itself, containing the variable z.
- 9: This is a constant term, so it does not count as a variable term.
Now, we can count the variable terms:
- From 3x³y: 2 variables (x and y)
- From 5x²: 1 variable (x)
- From 4y: 1 variable (y)
- From z: 1 variable (z)
Summing these up, we have:
- Variables in 3x³y: 2
- Variable in 5x²: 1
- Variable in 4y: 1
- Variable in z: 1
So to figure out the total number of unique variable terms:
- x appears in the first and second terms.
- y appears in the first and third terms.
- z is unique.
For the purpose of counting the number of variable terms, we only considered terms where a variable is present, regardless of how many times a specific variable is used. Therefore, accumulatively, we count:
- 3x³y (1 term with variables x and y)
- 5x² (1 term with variable x)
- 4y (1 term with variable y)
- z (1 term with variable z)
Thus, there are a total of 4 variable terms in the expression 3x³y + 5x² + 4y + z + 9.