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The image presents a section on **Factoring Algebraic Expressions**. Specifically, under the heading **Activity (IV)**, you are asked to "Factor completely" the following numbers:

1. 12
2. 42
3. 56
4. 100
5. 120

I will help you by factoring each number completely into its prime factors:

1. **12**  
   \(12 = 2^2 \times 3\)

2. **42**  
   \(42 = 2 \times 3 \times 7\)

3. **56**  
   \(56 = 2^3 \times 7\)

4. **100**  
   \(100 = 2^2 \times 5^2\)

5. **120**  
   \(120 = 2^3 \times 3 \times 5\)

These are the prime factorizations of each number listed.

Would you like further explanations on these or other factoring problems?

Here are 5 related questions to expand your understanding:
1. How do you use prime factorization to find the greatest common divisor (GCD) of two numbers?
2. How can prime factorization help in simplifying fractions?
3. What are composite numbers, and how do they differ from prime numbers?
4. How does prime factorization assist in solving least common multiple (LCM) problems?
5. How can prime factorizations be used in algebraic expressions?

**Tip:** Always begin by dividing the number by the smallest prime number (2) and continue with the next smallest primes until you reach 1.

Factor completely the following numbers: 12, 42, 56, 100, 120.

Learn how to factor completely the numbers 12, 42, 56, 100, and 120 using prime factorization. This exercise covers essential number theory concepts and the Fundamental Theorem of Arithmetic. Suitable for students in Grades 6-8.

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