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Calculus III

Course: Intermediate Algebra
Topic: Factoring
Subtopic: Special Forms & General Strategy

Overview

This last section on factoring polynomial expressions requires using three factoring formulas: difference of squares, difference of cubes, and sum of cubes.

• Caution: a binomial squared like (x+3)^2 must be FOILed out to get the "perfect square trinomial" x^2+6x+9 - never take the power across the addition to get x^2+3^2! Keeping this in mind will help you recognize PSTs when working backwards to factor into a binomial squared.
• If the original poly has only two terms then it factors as either a difference of squares, difference of cubes, or sum of cubes. These formulas are worth memorizing.
• Sum of squares are PRIME! E.g. x^2+9 cannot be factored (well, not until we cover imaginary numbers).
• Factoring polynomials enables us to solve polynomial equations via the zero product rule. The "zero products rule" is only applicable to equations not expressions. That is, you cannot "solve" the expression x^2+6x+9, all you can do is factor it.

Objectives

By the end of this topic you should know and be prepared to be tested on:

• 7.3.1 Recognize perfect square trinomials and be able to factor them down as a binomial squared
• 7.3.2 Recognize difference of squares and be able to factor them down including repeated difference of squares
• 7.3.3 Know that sum of squares can't be factored assuming any GCF is already factored out
• 7.3.4 Recognize sum/difference of cubes and be able to factor them down according to the formulas

Terminology & Supplemental Resources

Terms you should be able to define: binomial squared, PST = perfect square trinomial, difference of squares, sum/difference of cubes

MEMORIZE at least the first two of these factoring formulae:

Looking for a sheet with all the factoring formulae? Below are some suggestions from which to choose.