Factoring by Grouping Techniques

The video tutorial explains the process of factoring by grouping, a method used to factor polynomials with four terms. It begins with a correction to an initial mistake and proceeds with three examples, each demonstrating the step-by-step process of grouping terms, identifying the greatest common factor (GCF), and factoring out common terms. The tutorial emphasizes the importance of ensuring that the grouped terms have a common factor and concludes with a successful factorization of each example.

What is the first step in factoring by grouping?

• Combine all terms into one group

• Identify the greatest common factor (GCF) of all terms

• Multiply all terms together

• Form groups of two terms each

What correction was made to the initial problem?

• Changing 3x squared to 9x squared

• Changing 9x squared to 3x squared

• Changing 3x cubed to 9x cubed

• Changing 9x cubed to 3x cubed

What is the GCF of the first group of terms in the first example?

• x

• 3x

• 3x squared

• 9x squared

After factoring out the GCF from the first group, what is left inside the parentheses?

• x + 2

• x + 7

• x + 3

• x + 5

What is the GCF of the second group of terms in the first example?

• x squared

• x

• 2

• 3

What do you get when you factor out the common term from both groups in the first example?

• x + 5

• x + 7

• x + 2

• x + 3

In the second example, what is the GCF of the first group of terms?

• 3x

• x squared

• 3x squared

• x

What is the GCF of the second group of terms in the second example?

• x

• negative x

• negative 7

• 7

In the third example, what is the GCF of the first group of terms?

• 3

• 2x

• 2

• 3x

What is the GCF of the second group of terms in the third example?

• 3xy

• 3

• 3x

• 3y