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To factor the quadratic expression \(x^2 + 5x + 4\), we look for two numbers that multiply to 4 (the constant term) and add to 5 (the coefficient of the linear term).

The numbers 1 and 4 fit this requirement because:

- \(1 \times 4 = 4\) (the constant term)
- \(1 + 4 = 5\) (the coefficient of the linear term)

Therefore, the factored form of the expression is:

\[
x^2 + 5x + 4 = (x + 1)(x + 4)
\]

So, the answer is:

\[
(x + 1)(x + 4)
\]

Would you like any additional details or have any questions?

Here are some related questions you might find helpful:

1. How do you factor a quadratic expression when the coefficient of \(x^2\) is not 1?
2. What are the steps for factoring by grouping?
3. How can you verify if your factorization of a quadratic expression is correct?
4. How do you factor expressions where the constant term is negative?
5. What if the quadratic expression cannot be factored using integers?

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

Learn how to factor the quadratic expression x^2 + 5x + 4 with a step-by-step guide. This lesson covers essential algebraic techniques, including factoring methods suitable for middle school students in Grades 7-9.

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