Factor the following expression by grouping.
xy plus 6 x plus 5 y plus 30xy+6x+5y+30
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Part 1
Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.
A.
xy plus 6 x plus 5 y plus 30xy+6x+5y+30equals=enter your response here ​(Factor completely.)
B.
The polynomial cannot be factored.

Let's factor the expression by grouping. The given expression is:

\[
xy + 6x + 5y + 30
\]

1. **Group the terms** in pairs:
   \[
   (xy + 6x) + (5y + 30)
   \]

2. **Factor out the common factor** from each group:
   \[
   x(y + 6) + 5(y + 6)
   \]

3. Notice that \((y + 6)\) is a common factor. So, factor \((y + 6)\) out:
   \[
   (x + 5)(y + 6)
   \]

Thus, the expression can be factored as:

\[
(x + 5)(y + 6)
\]

So, the correct choice is:

**A.** \( xy + 6x + 5y + 30 = (x + 5)(y + 6) \)

Would you like more details on the steps? Here are 5 related questions:

1. How do you recognize when to factor by grouping?
2. What should you do if the terms can't be easily grouped?
3. Can all polynomials be factored by grouping?
4. What is the importance of identifying common factors?
5. How does factoring by grouping relate to solving quadratic equations?

**Tip:** When factoring by grouping, always check to see if the factors can be factored further.

Learn how to factor the expression xy + 6x + 5y + 30 using the grouping method with a detailed step-by-step solution. This problem covers key algebraic concepts, including factoring by grouping. Suitable for students in Grades 7-9.

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