Prime Factorization and GCF Problems

The video tutorial explains how simplifying rational expressions is similar to simplifying fractions by removing common factors between the numerator and denominator. It demonstrates this process using prime factorization with examples involving the numbers 28, 56, 32, and 48. The tutorial emphasizes the importance of identifying common factors and using the greatest common factor for simplification. It concludes with a preview of more examples in future videos.

What is the first step in simplifying rational expressions?

• Finding the greatest common factor

• Adding the numerator and denominator

• Subtracting the numerator from the denominator

• Identifying common factors between numerator and denominator

What is the prime factorization of 28?

• 2 x 14

• 2 x 2 x 7

• 4 x 7

• 2 x 3 x 7

How can 56 be expressed using prime factors?

• 2 x 3 x 9

• 2 x 2 x 2 x 7

• 7 x 8

• 4 x 14

What is the simplified form of 28x/56x using prime factorization?

• 1/2

• 1/3

• 3/4

• 2/3

What is the greatest common factor of 28 and 56?

• 14

• 28

• 7

• 56

How many factors of 2 are there in the prime factorization of 32?

• 6

• 5

• 3

• 4

What is the prime factorization of 48?

• 2 x 2 x 3 x 3

• 2 x 2 x 2 x 2 x 3

• 2 x 2 x 2 x 2 x 2

• 2 x 2 x 2 x 3

What is the simplified form of 32x^3y/48xy^2 using prime factorization?

• 2x^2/y

• 2x^2/3y

• x^2/2y

• 3x^2/2y

What is the greatest common factor of 32 and 48?

• 24

• 16

• 32

• 8

What is the simplified form of 32x^3y/48xy^2 using the greatest common factor?

• x^2/3y

• 2x^2/3y

• x^2/2y

• 3x^2/2y