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The image shows a mathematical expression that appears to be a polynomial that needs to be factored or simplified. The expression is:

\[
15x^5 - 25x^3 + 5x^2
\]

### Step-by-Step Solution:

1. **Factor Out the Greatest Common Factor (GCF):**
   First, identify the greatest common factor in all the terms. In this case, all terms share a factor of \(5x^2\).

   \[
   15x^5 - 25x^3 + 5x^2 = 5x^2(3x^3 - 5x + 1)
   \]

2. **Check for Further Factoring:**
   The expression inside the parentheses, \(3x^3 - 5x + 1\), does not appear to be factorable further using elementary methods. Therefore, the factored form of the expression is:

   \[
   5x^2(3x^3 - 5x + 1)
   \]

This is the simplest form of the expression.

Would you like more details on any step, or do you have any questions?

Here are five related questions:
1. How do you identify the greatest common factor in a polynomial?
2. What are the common methods for factoring polynomials?
3. Can the expression \(3x^3 - 5x + 1\) be factored further?
4. How would you approach factoring a polynomial of a higher degree, such as a 4th or 5th degree polynomial?
5. What is the importance of factoring in solving polynomial equations?

**Tip:** When factoring polynomials, always start by checking for a greatest common factor (GCF) across all terms. This simplifies the problem significantly.

Factor the expression 15x^5 - 25x^3 + 5x^2.

Learn how to factor the polynomial expression 15x^5 - 25x^3 + 5x^2 by identifying and applying the greatest common factor (GCF). This problem is ideal for students in Grades 9-11 who are studying polynomial factorization.

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