The given quadratic expression is:

\[
x^2 + 10x + 16
\]

To solve this, we can try factoring or using the quadratic formula. First, let's check if it can be factored.

### Step 1: Factoring
We are looking for two numbers that multiply to 16 (the constant term) and add to 10 (the coefficient of the linear term).

Factors of 16 are:  
\( 1 \times 16 \)  
\( 2 \times 8 \)  
\( 4 \times 4 \)

Out of these, \( 2 + 8 = 10 \), so we can factor the quadratic expression as:

\[
(x + 2)(x + 8)
\]

### Step 2: Solutions
If we set the expression equal to zero to solve for \(x\):

\[
(x + 2)(x + 8) = 0
\]

Then, the solutions are:
\[
x = -2 \quad \text{or} \quad x = -8
\]

Would you like more details about factoring, or do you have any questions?

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Here are 5 related questions you might find useful:
1. How would the solution change if the constant term was different?
2. Can all quadratics be factored, or when should we use the quadratic formula?
3. How do we verify if our factored form is correct?
4. What is the relationship between factoring and the graph of the quadratic equation?
5. How do we solve quadratics with coefficients larger than 1?

**Tip:** Always double-check your factored expression by expanding it to ensure it matches the original quadratic.

Explore how to factor and solve the quadratic equation x^2 + 10x + 16 using basic algebraic techniques. This step-by-step guide covers factoring methods and solutions for middle school students, focusing on key concepts of algebra and quadratic equations. Suitable for Grades 7-9.

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