# 7.5 General Strategy for Factoring Polynomials

### Learning Objectives

By the end of this section, you will be able to:

• Recognize and use the appropriate method to factor a polynomial completely

### Recognize and Use the Appropriate Method to Factor a Polynomial Completely

You have now become acquainted with all the methods of factoring that you will need in this course. (In your next algebra course, more methods will be added to your repertoire.) The figure below summarizes all the factoring methods we have covered. Figure 7.4 outlines a strategy you should use when factoring polynomials.

### How To

#### Factor polynomials.

• Step 1. Is there a greatest common factor?
• Factor it out.
• Step 2. Is the polynomial a binomial, trinomial, or are there more than three terms?
• If it is a binomial:
Is it a sum?
• Of squares? Sums of squares do not factor.
• Of cubes? Use the sum of cubes pattern.Is it a difference?
• Of squares? Factor as the product of conjugates.
• Of cubes? Use the difference of cubes pattern.
• If it is a trinomial:
Is it of the form x2+bx+c? Undo FOIL.
Is it of the form ax2+bx+c?
• If a and c are squares, check if it fits the trinomial square pattern.
• Use the trial and error or “ac” method.
• If it has more than three terms:
Use the grouping method.
• Step 3. Check.
• Is it factored completely?
• Do the factors multiply back to the original polynomial?

Remember, a polynomial is completely factored if, other than monomials, its factors are prime!

### Section 7.5 Exercises

#### Practice Makes Perfect

Recognize and Use the Appropriate Method to Factor a Polynomial Completely

In the following exercises, factor completely.

Everyday Math

#### Self Check

ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section. ⓑ Overall, after looking at the checklist, do you think you are well-prepared for the next section? Why or why not?