Factor by Grouping Techniques

Mrs. Angel teaches factor by grouping, a method for factoring polynomials with four terms. She explains the process through three examples, highlighting the importance of finding common binomial factors. The lesson covers handling subtraction and emphasizes checking work by multiplying back to the original polynomial.

What is the first step in factor by grouping?

• Break the polynomial into two binomials

• Find the common factor of all terms

• Multiply all terms together

• Combine all terms into one group

In the first example, what is the greatest common factor of the first binomial?

• n

• n^3

• 2

• n^2

What must be true for factor by grouping to work?

• All terms must be even

• There must be a common binomial factor

• The polynomial must have three terms

• All terms must be positive

Why do we change subtraction into adding a negative in the second example?

• To make the polynomial shorter

• Because groups can only be formed in expressions with addition

• To simplify the multiplication

• To make the polynomial longer

What is the greatest common factor of the first binomial in the second example?

• 5

• 3x

• 6x^2

• 4

In the second example, what is factored out from the second binomial?

• Positive 4

• Negative 5

• Negative 4

• Positive 5

What should you do if you can't find a greatest common factor in a binomial?

• Skip the binomial

• Divide the binomial by 2

• Multiply the binomial by 2

• Factor out 1 or -1

In the third example, what is factored out from the second binomial?

• 6

• 1

• 6v^2

• 5z

What is the final step in factor by grouping?

• Divide the polynomial by the common factor

• Combine the greatest common factors into one binomial

• Add all terms together

• Multiply all terms together

What should you do if you don't have a common binomial factor after factoring?

• Go back to step one

• Go back to step two and recheck the greatest common factors

• Skip the problem

• Multiply the binomials together