Factoring Polynomials by Grouping Techniques

The video tutorial explains how to factor an expression by grouping, a method used when dealing with four terms that do not share a common factor. The instructor demonstrates the process of grouping the first two and last two terms, factoring out the greatest common factor (GCF) from each group, and ensuring the resulting expressions are identical. The tutorial provides tips on rearranging terms if necessary and concludes with a successful example of factoring by grouping.

What is the primary reason for using grouping in factoring expressions?

• To rearrange the terms

• To solve the equation

• To factor out the GCF from four terms

• To simplify the expression

What is the first step in factoring by grouping?

• Group the first two and last two terms

• Factor out the GCF from all terms

• Rearrange the terms

• Solve the equation

Why is it important to group terms that share a common factor?

• To ensure the problem is factorable

• To solve the equation

• To simplify the expression

• To rearrange the terms

What is the GCF of the terms 3X and 3Y?

• 3X

• Y

• 3

• X

What should you do if the grouped terms do not share a common factor?

• Rearrange the terms

• Factor out the GCF

• Solve the equation

• Simplify the expression

What should you check after factoring out the GCF from grouped terms?

• If the equation is solved

• If the resulting expressions are the same

• If the terms are rearranged

• If the expression is simplified

What should you do if the resulting expressions after factoring out the GCF are not the same?

• Simplify the expression

• Rearrange the terms

• Factor out the GCF again

• Solve the equation

What is the GCF of the terms -7Y and -7X?

• -7Y

• X

• Y

• -7

What is the final step in factoring by grouping?

• Simplify the expression

• Verify the factored expression

• Factor out the GCF from the entire expression

• Rearrange the terms

What is the result after factoring out the common term from the expression (3X - 7)(Y - 8X)?

• 3X + 7

• Y - 8X

• 3X - 7

• (3X - 7)(Y - 8X)