Factoring Four-Term Polynomials by Grouping

The video tutorial covers the process of factoring polynomials, focusing on the method of grouping. It begins with an introduction to factoring and the importance of identifying the greatest common factor. The tutorial then provides a detailed example of factoring by grouping, including handling negative signs and cases where the common factor is one. Advanced techniques and considerations are also discussed to ensure accurate factoring.

What is the first step in factoring any polynomial?

• Multiply the terms

• Take out the greatest common factor

• Count the number of terms

• Group the terms

When factoring by grouping, what should you do if there are four terms?

• Use the quadratic formula

• Group the first two and the last two terms

• Factor out the greatest common factor

• Combine all terms into one

In the example given, what is the common factor of the first group of terms?

• X

• 7

• X squared

• 3

What must be true about the binomials in each group for the problem to factor by grouping?

• They must match exactly

• They must be multiplied

• They must be different

• They must be prime

What is the greatest common factor in the second group of terms in the example?

• 3

• X squared

• 7

• X

What should you do if the binomials do not match after factoring out the common factors?

• Rearrange the original problem

• Multiply the terms

• Add a constant

• Divide by the common factor

How should you handle a minus sign in front of the third term when factoring by grouping?

• Add it to the first term

• Factor out a positive number

• Factor out a negative number

• Ignore it

What is the common factor in the example where the only common factor is one?

• X squared

• X

• 5

• 1

What should you do if the terms in a group do not share any common factors?

• Divide by the greatest common factor

• Multiply the terms

• Combine the terms

• Factor out a 1

What is the final step to ensure your factoring by grouping is correct?

• Divide the terms

• Add the terms

• Multiply the terms

• Check by multiplying out the binomials