Factoring Expressions and Common Terms

The video tutorial explains the method of factoring by grouping, which involves grouping terms, factoring out common monomials, and then factoring out common binomials. Several examples are provided to illustrate the process, including polynomials with different structures and operations. The tutorial emphasizes the importance of identifying common factors and changing operations when necessary.

What is the first step in factoring by grouping?

• Factor out the common binomial

• Group the first two terms together and the next two terms together

• Factor out the common monomial

• Divide each term by the common binomial

In the example ax + ay + bx + by, what is the common binomial?

• a + b

• x + y

• bx + by

• ax + ay

What is the common monomial in the expression 3x^3 + 6x^2?

• 6x^2

• 3x^2

• x^2

• 3x

After factoring out the common binomial in 3x^3 + 6x^2 + 5x + 10, what are the factors?

• x + 2 and 3x + 10

• x + 2 and 3x^2 + 10

• x + 2 and 3x + 5

• x + 2 and 3x^2 + 5

In the expression x^2 + xy - 4x - 4y, what is the common binomial?

• x^2 - 4x

• x - 4

• x + y

• xy - 4y

What is the common monomial in the expression x^2 + xy?

• x

• y

• x^2

• xy

In the expression XY + 7x - 7y - 49, what should you remember to change?

• Division to multiplication

• Multiplication to division

• Subtraction to addition

• Addition to subtraction

What is the common binomial in the expression XY + 7x - 7y - 49?

• y + 49

• y + 7

• 7x - 7y

• XY + 7x

In the expression 4x^4 - 2x^3 - 6x + 3, what is the common monomial in the first group?

• 2x

• 4x^4

• 2x^3

• 6x

What are the factors of the expression 4x^4 - 2x^3 - 6x + 3?

• 2x - 1 and 4x^3 - 3

• 2x - 1 and 2x^3 + 3

• 2x - 1 and 2x^3 - 3

• 2x - 1 and 4x^3 + 3