Question
When dividing 4x+2y-8/2b how many variables will be present in the quotient
Answers
GPT-4o mini
When you divide \( 4x + 2y - 8 \) by \( 2b \), you're performing the operation of polynomial long division. The expression \( 4x + 2y - 8 \) is a polynomial in terms of the variables \( x \) and \( y \), and \( 2b \) is a term involving a different variable \( b \).
When you perform the division, the resulting quotient will also be a polynomial involving the same variables as in the original polynomial since you are dividing by a coefficient. The resulting expression can be simplified:
\[
\frac{4x + 2y - 8}{2b} = \frac{4x}{2b} + \frac{2y}{2b} - \frac{8}{2b}
\]
This simplifies to:
\[
\frac{2x}{b} + \frac{y}{b} - \frac{4}{b}
\]
In this expression, the variables present are \( x \), \( y \), and \( b \).
So, in total, there are **three variables** in the quotient: \( x \), \( y \), and \( b \).
When you perform the division, the resulting quotient will also be a polynomial involving the same variables as in the original polynomial since you are dividing by a coefficient. The resulting expression can be simplified:
\[
\frac{4x + 2y - 8}{2b} = \frac{4x}{2b} + \frac{2y}{2b} - \frac{8}{2b}
\]
This simplifies to:
\[
\frac{2x}{b} + \frac{y}{b} - \frac{4}{b}
\]
In this expression, the variables present are \( x \), \( y \), and \( b \).
So, in total, there are **three variables** in the quotient: \( x \), \( y \), and \( b \).