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Let's factor the quadratic expression \( x^2 + 8x + 7 \).

We are looking for two numbers that multiply to give \( 7 \) (the constant term) and add to give \( 8 \) (the coefficient of \( x \)).

The two numbers that work are \( 7 \) and \( 1 \), because:

\[
7 \times 1 = 7 \quad \text{and} \quad 7 + 1 = 8.
\]

Thus, we can factor the quadratic expression as:

\[
x^2 + 8x + 7 = (x + 7)(x + 1).
\]

So, the factored expression is \( (x + 7)(x + 1) \).

Would you like further details or have any other questions?

Here are some related questions:
1. How do you factor more complex quadratics?
2. What is the quadratic formula, and when do you use it?
3. How can you verify that your factored form is correct?
4. What does it mean if a quadratic cannot be factored using integers?
5. How do you factor quadratics with a leading coefficient greater than 1?

**Tip:** Always check your factors by expanding them to ensure they multiply back to the original quadratic expression!

Learn how to factor the quadratic equation x^2 + 8x + 7 by finding two numbers that multiply to 7 and add to 8. This is a key algebraic concept suitable for students in Grades 7-9.

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