When dividing the expression \(4x + 2y - 8\) by \(2b\), you perform the division on each term of the polynomial.
The quotient can be written as:
\[ \frac{4x}{2b} + \frac{2y}{2b} - \frac{8}{2b} \]
Now, simplifying each term:
- \(\frac{4x}{2b} = \frac{4}{2} \cdot \frac{x}{b} = 2 \cdot \frac{x}{b}\)
- \(\frac{2y}{2b} = \frac{2}{2} \cdot \frac{y}{b} = 1 \cdot \frac{y}{b} = \frac{y}{b}\)
- \(\frac{8}{2b} = \frac{8}{2} \cdot \frac{1}{b} = 4 \cdot \frac{1}{b} = \frac{4}{b}\)
Combining these, the simplified form of the quotient is:
\[ \frac{2x}{b} + \frac{y}{b} - \frac{4}{b} \]
In this expression, the variables present are \(x\), \(y\), and \(b\). Therefore, there are three variables in the quotient.