Factor by Grouping Techniques for Multiple Terms

The video tutorial covers the method of factoring by grouping, starting with four or more terms. It explains the importance of identifying the greatest common factor (GCF) and demonstrates the process through multiple examples. The tutorial also addresses the need to rearrange terms for effective grouping and explores different strategies for factoring expressions with six terms. The video concludes with a final example, emphasizing the importance of checking for further factorization opportunities.

What is the first step in factoring any expression?

• Rearranging terms

• Identifying the greatest common factor

• Grouping terms

• Factoring trinomials

When grouping terms, what should you do if the terms do not have a common factor?

• Skip the term

• Rearrange the terms

• Factor out a 1

• Use a different method

In the example with four terms, what is the GCF of the first two terms?

• 5x^2

• 10x^2

• 15x

• 5x

Why is it important to include the plus sign when factoring out a positive number?

• To simplify the expression

• To separate terms

• To ensure the expression is equivalent

• To indicate addition

What should you do if the terms in the expression are not in standard form?

• Rearrange the terms

• Factor out a 1

• Use a different method

• Skip the problem

In the example with a GCF and standard form, what is the GCF of the entire expression?

• 16

• 4

• 8

• 2

When grouping six terms, what are the two possible grouping strategies?

• Three groups of two or two groups of four

• Two groups of three or four groups of one

• Three groups of two or four groups of one

• Two groups of three or three groups of two

What should you do if the parentheses do not match after grouping?

• Use a different method

• Rearrange the terms

• Factor out a 1

• Skip the problem

In the final example, what is the first factor after grouping the terms?

• k^2 - 4

• k^2 + 8k + 12

• k - 2

• k + 2

What is the final step in factoring a trinomial with a leading coefficient of one?

• Rearranging terms

• Factoring out the GCF

• Setting up two sets of parentheses

• Using the difference of squares