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To factor the expression \( 7x^2 + 5x \), we need to factor out the greatest common factor (GCF).

1. **Identify the GCF:** 
   The GCF of the terms \( 7x^2 \) and \( 5x \) is \( x \), as both terms have at least one factor of \( x \).

2. **Factor out the GCF:** 
   Factor \( x \) from both terms:
   \[
   7x^2 + 5x = x(7x + 5)
   \]

Thus, the correct factored form is **\( x(7x + 5) \)**.

The correct answer is the option: **\( x(7x + 5) \)**.

Would you like further details on this, or have any questions?

Here are 5 questions for further exploration:
1. How do you determine the greatest common factor in a polynomial?
2. What happens if the terms do not have a common factor?
3. Can the expression \( 7x^2 + 5x \) be factored any further?
4. How do you check if a polynomial is factorable?
5. What is the difference between factoring a quadratic and a higher-degree polynomial?

**Tip:** Always start by factoring out the greatest common factor before attempting other factoring techniques like grouping or applying formulas.

Which of the following is the correct factored form for the given expression: 7x^2 + 5x

Learn how to factor the polynomial 7x^2 + 5x by identifying and factoring out the greatest common factor (GCF). This problem covers key algebraic concepts suitable for students in Grades 8-10.

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