Mara carried water bottles to the field to share with her team at halftime. The water bottles weighed a total of 60*x*2 + 48*x* + 24 ounces.

Which factorization could represent the number of water bottles and weight of each water bottle?

6(10*x*2 + 8*x* + 2)

12(5*x*2 + 4*x* + 2)

6*x*(10*x*2 + 8*x* + 2)

12*x*(5*x*2 + 4*x* + 2)

To find the correct factorization that represents the number of water bottles and the weight of each water bottle, we can start by factoring the expression \(60x^2 + 48x + 24\).

1. **Find the greatest common factor (GCF):**

   The coefficients of the terms are 60, 48, and 24. The GCF of these numbers is:

   \[
   \text{GCF}(60, 48, 24) = 12
   \]

   All terms have a factor of 12, and since there are no common \(x\) factors in all terms, the GCF is just 12.

2. **Factor out the GCF:**

   Factor out 12 from each term in the expression:

   \[
   60x^2 + 48x + 24 = 12(5x^2 + 4x + 2)
   \]

   This expression cannot be factored further with the coefficients being integers.

Therefore, the correct factorization of \(60x^2 + 48x + 24\) is:

\[
\boxed{12(5x^2 + 4x + 2)}
\]

Among the given options, this matches option **2**: \(12(5x^2 + 4x + 2)\).

---

Would you like further details or have any questions about this factorization process?

Here are five related questions to expand your understanding:

1. How do you find the greatest common factor (GCF) of three or more numbers?
2. What is the factored form of \(18x^2 + 24x + 6\)?
3. Can you explain why \(12x(5x^2 + 4x + 2)\) is not the correct factorization for \(60x^2 + 48x + 24\)?
4. How can you verify if a factorization is correct?
5. Why is it important to factor out the greatest common factor first when factoring a polynomial?

**Tip:** Always check for a common factor in all terms of a polynomial before attempting to factor further. This will simplify the expression and make further factorization easier.

Learn how to factor the polynomial 60x^2 + 48x + 24 using the greatest common factor (GCF) method. This problem involves factoring a quadratic expression and simplifying it to find the correct factorization. Suitable for Grades 7-9 students learning about polynomial factorization.

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