Factoring Techniques and Concepts

The video tutorial explains how to factor polynomials with four terms using the method of grouping. The instructor begins by introducing the concept and emphasizes the importance of recognizing when to use this technique. The process involves grouping the first two terms and the last two terms separately, then factoring out common factors from each group. The tutorial provides a step-by-step demonstration, highlighting key transitions and common challenges students may face. By the end, viewers should understand how to factor by grouping and apply this method to similar problems.

What should you automatically think of when you see four terms in an expression?

• Factoring by grouping

• Factoring by division

• Factoring by substitution

• Factoring by expansion

What is the first step in factoring by grouping?

• Factor out the greatest common factor

• Combine like terms

• Expand the expression

• Group the first two terms and the last two terms

What can be factored out from the terms 4X^3 - 20X^2?

• 4X^2

• X^2

• 20X

• 4X

What common factor do the terms 7X and -35 share?

• X

• 35

• 7

• 5

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

• Factor out the common numerical factor

• Divide the terms

• Combine like terms

• Expand the expression

What is the next step after factoring out common factors from each group?

• Combine like terms

• Expand the expression

• Factor out a common binomial factor

• Divide the terms

What binomial factor is common in the expression after grouping?

• 4X^2

• X - 5

• X + 5

• 7

What is left over after factoring out the common binomial factor X - 5?

• X^2 + 7

• 4X^2 + 7

• 4X^2 - 7

• 4X + 7

How can the expression be written after factoring out the common binomial factor?

• (X - 5)(4X + 7)

• (X + 5)(4X^2 + 7)

• (X - 5)(4X^2 + 7)

• (X + 5)(4X + 7)

What is the purpose of factoring by grouping?

• To expand expressions

• To simplify expressions with four terms

• To divide terms

• To combine like terms