To factor the quadratic expression \( x^2 - 11x + 24 \), follow these steps:

1. We need to find two numbers that multiply to \( 24 \) (the constant term) and add up to \( -11 \) (the coefficient of \( x \)).

2. The pair of numbers that satisfies this condition is \( -3 \) and \( -8 \), because:
   \[
   -3 \times -8 = 24 \quad \text{and} \quad -3 + -8 = -11
   \]

3. Therefore, we can factor the quadratic as:
   \[
   (x - 3)(x - 8)
   \]

So, the factored form of \( x^2 - 11x + 24 \) is:
\[
(x - 3)(x - 8)
\]

Would you like more details or have any questions?

Here are 5 related questions to explore:
1. How do you factor a quadratic when the leading coefficient is not 1?
2. Can all quadratics be factored using integers?
3. What is the quadratic formula, and how is it used for factoring?
4. How would you graph \( x^2 - 11x + 24 \) and its factors?
5. What does it mean if a quadratic cannot be factored easily?

**Tip:** Always check the discriminant (\( b^2 - 4ac \)) to determine if a quadratic is factorable with real numbers!

Learn how to factor the quadratic equation x^2 - 11x + 24 using the product-sum method. This step-by-step solution explains the key concepts of factoring trinomials and covers important algebraic techniques. Suitable for students in Grades 8-10.

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