Factoring by Grouping Techniques

The video tutorial explains the factoring technique known as factoring by grouping. It begins with an introduction to the concept, followed by two detailed examples demonstrating the process. The tutorial highlights the importance of identifying common factors and provides guidelines on when to use this technique effectively. The video emphasizes that factoring by grouping is useful when there are four terms with no common factor among all terms, and it may require rearranging terms to identify common factors.

Why is factoring by grouping used?

• To solve equations with three terms

• To eliminate all variables in an equation

• To divide terms into groups and find common factors within each group

• To simplify equations with a common factor among all terms

In the first example, what is the common factor in the terms M squared and MN?

• There is no common factor

• M

• 4

• N

What is the common factor in the terms 4m and 4n?

• M

• N

• 4

• There is no common factor

After factoring out the common factors in the first example, what is the final factored form?

• M(M - N) - 4(M - N)

• M(M - N) + 4(M - N)

• M(M + N) + 4(M + N)

• M(M + N) - 4(M + N)

What hypothetical variable is used to explain the common factor concept?

• W

• X

• Z

• Y

In the second example, what is the common factor in the terms 3x and 12?

• X

• 3

• 4

• There is no common factor

Why is it important to consider the negative sign in the second example?

• It eliminates one of the terms

• It simplifies the equation

• It affects the final factored form

• It changes the common factor

What is the final factored form in the second example?

• 3(X - 4) - Y(X - 4)

• 3(X + 4) + Y(X + 4)

• 3(X - 4) + Y(X - 4)

• 3(X + 4) - Y(X + 4)

When should you use factoring by grouping?

• When there are three terms

• When there is a common factor among all terms

• When there are four terms and no common factor among all

• When the equation is already simplified

What should you do if the terms in the equation do not seem to have common factors?

• Rearrange the terms and try again

• Add more terms to the equation

• Give up on factoring

• Multiply all terms by a constant