To find the greatest common factor (GCF) of the expression \(5x^2 + 3x\), we need to identify the common factors in each term.

### Steps:
1. **Identify factors of each term**:
   - The first term, \(5x^2\), factors into \(5 \cdot x \cdot x\).
   - The second term, \(3x\), factors into \(3 \cdot x\).

2. **Find the common factors**:
   - The only common factor between the two terms is \(x\).

### Solution:
The GCF of \(5x^2 + 3x\) is \(x\).

### Factoring the Expression Using the GCF:
Now, we can factor out the GCF from the expression:
\[
5x^2 + 3x = x(5x + 3)
\]

Would you like more details on factoring or have any questions?

---

**Further Questions:**
1. How do you find the GCF of expressions with more terms?
2. What is the GCF of a polynomial with three or more terms?
3. How does the GCF affect simplification of rational expressions?
4. Can the GCF of a polynomial include more than just variables?
5. How is the GCF used when factoring quadratic equations?

**Tip:** Factoring out the GCF is often the first step in simplifying expressions and solving equations.

Explore how to find the greatest common factor (GCF) of the algebraic expression 5x^2 + 3x. This guide provides a step-by-step solution, covering core algebraic concepts of factoring and simplifying expressions. Ideal for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation