factor:%20%20-%2010r%20-%209q%20%5E%202%20+%2030q%20+%206qr%20-%2025

We are tasked with factoring the expression:

\[
-10r - 9q^2 + 30q + 6qr - 25
\]

### Step 1: Group terms
We begin by grouping the terms to facilitate factoring:

\[
(-9q^2 + 30q) + (6qr - 10r) - 25
\]

### Step 2: Factor out common factors from each group
- From \(-9q^2 + 30q\), we can factor out \(-3q\):
  \[
  -3q(3q - 10)
  \]

- From \(6qr - 10r\), we can factor out \(2r\):
  \[
  2r(3q - 5)
  \]

So the expression now looks like:
\[
-3q(3q - 10) + 2r(3q - 5) - 25
\]

### Step 3: Combine terms
The expression cannot be simplified further by common factoring because the terms do not share a factor in common across all terms.

Thus, the fully factored expression is:
\[
-3q(3q - 10) + 2r(3q - 5) - 25
\]

Let me know if you'd like further clarification or have any questions!

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Here are some related questions:
1. What is the distributive property of multiplication?
2. How do you factor trinomials?
3. What are the common factoring techniques in algebra?
4. How does factoring help in solving quadratic equations?
5. What is the difference between factoring and expanding expressions?

**Tip:** When factoring, always start by looking for common factors and grouping terms that

Learn how to factor the polynomial -10r - 9q^2 + 30q + 6qr - 25 step-by-step. This algebraic problem involves factoring by grouping and the distributive property. Suitable for students in Grades 9-11.

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