To factor the quadratic expression \( x^2 + 11x + 24 \), we need to find two numbers that:

1. Multiply to \( 24 \) (the constant term).
2. Add up to \( 11 \) (the coefficient of the \( x \) term).

The numbers \( 3 \) and \( 8 \) satisfy these conditions:

- \( 3 \times 8 = 24 \)
- \( 3 + 8 = 11 \)

So, we can factor the expression as:

\[
x^2 + 11x + 24 = (x + 3)(x + 8)
\]

Thus, the factors of \( x^2 + 11x + 24 \) are \( (x + 3) \) and \( (x + 8) \).

Would you like more details or have any questions?

Here are some additional questions to extend this topic:

1. What are the factors of a different quadratic, like \( x^2 + 10x + 25 \)?
2. How do we factor quadratic expressions where the coefficient of \( x^2 \) is not 1?
3. What method do we use if the quadratic expression cannot be factored by simple inspection?
4. How do you determine the roots of a quadratic equation using the quadratic formula?
5. Can we apply factoring to solve quadratic inequalities?

**Tip:** When factoring quadratics, always check if it can be factored by finding two numbers that satisfy both conditions for the middle and constant terms.

Learn how to factor the quadratic expression x^2 + 11x + 24 with a clear, step-by-step approach. Understand key algebra concepts such as factorization, finding factors, and the quadratic equation formula. Perfect for students in Grades 8-10.

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