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We are tasked with factoring the trinomial \( x^2 - 2x - 24 \), or determining if it is prime.

To factor the quadratic expression \( x^2 - 2x - 24 \), we need to find two numbers that multiply to \(-24\) and add to \(-2\).

1. Factors of \(-24\) are:
   - \( 1 \times -24 \)
   - \( -1 \times 24 \)
   - \( 2 \times -12 \)
   - \( -2 \times 12 \)
   - \( 3 \times -8 \)
   - \( -3 \times 8 \)
   - \( 4 \times -6 \)
   - \( -4 \times 6 \)

2. The pair that adds to \(-2\) is \( 4 \times -6 \).

Thus, we can factor the trinomial as:
\[
x^2 - 2x - 24 = (x - 6)(x + 4)
\]

So, the correct answer is **B) \( (x - 6)(x + 4) \)**.

Would you like more details on the factorization process, or do you have any questions?

### Related Questions:
1. How can you verify if a trinomial is prime?
2. What are the methods to factor more complex quadratics?
3. How do the signs of factors influence the factorization?
4. How can you solve quadratic equations using the factored form?
5. What are other methods to factor trinomials, such as completing the square?

### Tip:
Always check the product and sum of your factor pairs carefully to avoid simple mistakes in sign or arithmetic.

Factor the trinomial or state that the trinomial is prime: x^2 - 2x - 24

Learn how to factor the quadratic trinomial x^2 - 2x - 24 by finding two numbers that multiply to -24 and add up to -2. This guide explains step-by-step how to use factoring methods to solve quadratic equations, perfect for students in Grades 9-10.

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