Sure, let's solve the given problem step by step.
We need to perform the division of the polynomial [tex]\(a b + 3 a + 2 b + 6\)[/tex] by 5. Here's how we can approach this:
1. Write the polynomial to be divided by 5:
[tex]\(a b + 3 a + 2 b + 6\)[/tex]
2. Distribute the division across each term of the polynomial separately:
[tex]\[
\frac{a b}{5} + \frac{3 a}{5} + \frac{2 b}{5} + \frac{6}{5}
\][/tex]
3. Combine like terms where possible:
Each term here is distinct, so we keep them separate.
4. Rewrite the expression to group the terms involving similar variables:
Recall that when we are dividing by 5, each term in the original polynomial gets divided by 5 individually. Thus:
[tex]\[
\frac{a b}{5} + \frac{3 a}{5} + \frac{2 b}{5} + \frac{6}{5}
\][/tex]
This can also be written as:
[tex]\[
a \left( \frac{b}{5} + \frac{3}{5} \right) + \frac{2 b}{5} + \frac{6}{5}
\][/tex]
Therefore, the expression [tex]\(\frac{ab + 3a + 2b + 6}{5}\)[/tex] can be simplified to:
[tex]\[
a \left( \frac{b}{5} + \frac{3}{5} \right) + \frac{2b}{5} + \frac{6}{5}
\][/tex]
And this is the quotient obtained by dividing the given polynomial by 5.
