Understanding Greatest Common Factor and Factoring Binomials

The video tutorial explains how to identify and factor the greatest common factor (GCF) from binomials. It provides two examples: one with numerical coefficients and another with variables. The process involves finding the GCF by prime factorization and factoring out the GCF to simplify the binomial. The tutorial emphasizes the importance of recognizing common factors and provides a methodical approach to factoring binomials.

What is the Greatest Common Factor (GCF) of a binomial?

• The sum of the terms in the binomial

• The largest monomial that divides each term evenly

• The product of the terms in the binomial

• The smallest monomial that divides each term evenly

What is the GCF of the coefficients 4 and 12?

• 6

• 4

• 2

• 8

How can 4x^3 be expressed using prime factorization?

• 2 x 2 x x x x

• 4 x x x

• 2 x 3 x x x

• 2 x 2 x x x

After factoring out the GCF from 4x^3 + 12x, what is the remaining expression?

• x^3 + 4

• x^2 + 3

• x^3 + 3

• x^2 + 4

What is the GCF of 18 and 45?

• 12

• 6

• 3

• 9

Which of the following is part of the GCF for the variables in the second example?

• b^4

• a^2

• b^5

• a^4

What is the GCF of the terms 18a^4b^3 and 45a^2b^5?

• 9a^4b^5

• 18a^2b^3

• 9a^2b^3

• 18a^4b^5

After factoring out the GCF from the second example, what is the remaining expression?

• 2a^2 + 5b^2

• 2a^3 + 5b^3

• 3a^3 + 5b^3

• 3a^2 + 5b^2

What is the significance of the lowest exponent in the GCF?

• It determines the lowest power of the variable in the GCF

• It is always the same as the highest exponent

• It is ignored in the GCF calculation

• It determines the highest power of the variable in the GCF

What is the factored form of the binomial 18a^4b^3 + 45a^2b^5?

• 9a^2b^3(2a^2 + 5b^2)

• 9a^4b^5(2a^2 + 5b^2)

• 18a^4b^5(2a^2 + 5b^2)

• 18a^2b^3(2a^2 + 5b^2)