Factoring by Grouping: Techniques and Examples

The video tutorial explains the process of factoring by grouping, a method used when dealing with four terms. It begins by identifying when this method is applicable, then demonstrates how to group the first and last two terms. The tutorial continues by showing how to factor out the greatest common factor from each group and highlights the importance of recognizing common terms like 'two X minus one'. Finally, it discusses the potential for further factoring, such as the difference of squares, and notes when the process is complete.

When should you consider using the factoring by grouping method?

• When you have five terms.

• When you have two terms.

• When you have three terms.

• When you have four terms.

What should you do if the terms are separated by a minus sign?

• Ignore the minus sign.

• Treat it as a plus sign.

• Consider it as adding the opposite.

• Combine the terms.

What is the first step after grouping the terms?

• Add the groups together.

• Factor out the greatest common factor from each group.

• Multiply the groups.

• Subtract the groups.

What is the greatest common factor in the first group if the terms are x^2 and 2x?

• 2

• x^2

• x

• 2x

What do you do after factoring out the greatest common factor from each group?

• Subtract the groups.

• Add the groups together.

• Factor out the common binomial factor.

• Multiply the groups.

What is the common binomial factor in the example given?

• x^2

• 3

• 2x - 1

• x - 2

What is the result after factoring out the common binomial factor?

• 2x + 1

• x^2 - 3

• 2x - 1

• x^2 + 3

What should you check for after factoring out the common binomial factor?

• If the terms can be added.

• If the terms can be multiplied.

• If further factoring is possible.

• If the terms can be subtracted.

What is the next step if the remaining terms form a difference of two squares?

• Subtract the terms.

• Factor further.

• Multiply the terms.

• Add the terms.