Finding Common Factors of Monomials

The video tutorial explains how to find common factors in polynomials by listing each monomial as a product of its prime factors and identifying the common elements. It provides three examples to illustrate the process: 12x^2 and 15x^3, 24a^4 and 6a, and 81y^2 and 144y^3. The tutorial emphasizes the importance of prime factorization and finding the greatest common factor.

What is the first step in finding common factors of polynomials?

• Divide the monomials by their coefficients

• List each monomial as a product of its prime factors

• Multiply the monomials

• Add all the coefficients

What do you do after listing the prime factors of each monomial?

• Find the sum of all factors

• Subtract the smallest factor from the largest

• Identify the common elements

• Multiply all factors together

In the example of 12x^2 and 15x^3, what is the greatest common factor?

• 5x^3

• 3x^2

• 6x^2

• 3x^3

What are the prime factors of 12x^2?

• 2, 2, 3, x^2

• 3, 5, x^3

• 2, 3, 5, x

• 2, 2, 5, x^2

Which of the following is a common factor of 12x^2 and 15x^3?

• 5

• x^3

• 2

• 3

What is the greatest common factor of 12x^2 and 15x^3?

• 3x^2

• 6x^3

• 12x^2

• 15x^3

Which of the following is a prime factor of 12x^2?

• 3

• 5

• 11

• 7

What is the common factor of 12x^2 and 15x^3?

• 5x

• x^3

• 2x

• 3x^2

In the example of 24a^4 and 6a, what is the greatest common factor?

• 12a^2

• 6a

• 24a^4

• 3a

What are the prime factors of 24a^4?

• 2, 2, 2, 3, a^4

• 3, 2, a

• 2, 3, 5, a^2

• 2, 2, 3, a^3