Understanding Greatest Common Factor of Monomials

The video tutorial explains how to find the greatest common factor (GCF) of monomials by breaking each term into its simplest components, such as prime factors for numbers and individual variables for expressions. The process is demonstrated with three examples: 10cd², 5cd, and 25c³d². The GCF is identified by finding the common elements in the factorized forms of these monomials, resulting in 5cd as the greatest common factor.

What is a monomial?

• A one-term expression

• A multi-term expression

• An expression with two variables

• An expression with no variables

What is the first step in finding the greatest common factor of monomials?

• Divide the terms by the smallest coefficient

• Break down each term into its simplest components

• Add the coefficients

• Multiply the terms

What is the prime factorization of 10?

• 2 x 3

• 2 x 5

• 5 x 5

• 3 x 5

How can d² be expressed in terms of its simplest components?

• d x d

• 2d

• d²

• d + d

What is the prime factorization of 5?

• 5 x 5

• 5

• 2 x 5

• 1 x 5

What is the prime factorization of 25?

• 5 x 10

• 3 x 5

• 2 x 5

• 5 x 5

How can c³ be expressed in terms of its simplest components?

• c x c x c

• c³

• c + c + c

• 3c

Which of the following is a common factor in all three monomials?

• 2

• d²

• c²

• 5

What is the greatest common factor of the monomials 10cd², 5cd, and 25c³d²?

• 5cd

• 25cd

• 5c²d²

• 10cd

Why can't the greatest common factor be larger than 5cd?

• Because 5cd is the largest factor of 5cd

• Because 5cd is not common

• Because 5cd is the smallest factor

• Because 5cd is not a factor