To solve the quadratic expression \(x^2 + 7x + 10\), we can factor it.

### Step-by-Step Solution:

1. **Identify the coefficients:**  
   The quadratic expression is in the form \(ax^2 + bx + c\), where:  
   \(a = 1\), \(b = 7\), and \(c = 10\).

2. **Find two numbers that multiply to \(c\) (10) and add up to \(b\) (7):**  
   The numbers are 5 and 2 since \(5 \times 2 = 10\) and \(5 + 2 = 7\).

3. **Rewrite the quadratic expression as a product of two binomials:**  
   The expression can be factored as:  
   \[
   x^2 + 7x + 10 = (x + 5)(x + 2)
   \]

### Factored Form:

\[
x^2 + 7x + 10 = (x + 5)(x + 2)
\]

### Verification:

To verify the factorization, expand the factored form:

\[
(x + 5)(x + 2) = x^2 + 2x + 5x + 10 = x^2 + 7x + 10
\]

The expanded form matches the original quadratic expression.

### Conclusion:

The quadratic expression \(x^2 + 7x + 10\) factors to \((x + 5)(x + 2)\).

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Would you like more details on this solution, or do you have any specific questions?

Here are 5 related questions you might find interesting:

1. How do you solve the equation \(x^2 + 7x + 10 = 0\)?
2. What are the roots of the quadratic equation \(x^2 + 7x + 10 = 0\)?
3. How do you use the quadratic formula to solve \(x^2 + 7x + 10 = 0\)?
4. Can all quadratic expressions be factored easily? What is the difference between factorizable and irreducible quadratics?
5. How does completing the square work for the quadratic expression \(x^2 + 7x + 10\)?

**Tip:** When factoring quadratics, always look for two numbers that multiply to the constant term \(c\) and add to the coefficient of the linear term \(b\).

Learn how to factor the quadratic equation x^2 + 7x + 10 using the factoring method. This step-by-step guide covers key concepts in algebra, including finding numbers that multiply to the constant term and add to the linear coefficient. Ideal for students in Grades 7-9.

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