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12 Factoring Polynomials
In this chapter, you learn about factoring polynomials.
Factoring and Its Objectives
Factoring is the process of undoing
multiplication, so you need a strong
understanding of multiplication of
polynomials to be skillful in factor-
ing them. You can expect that, from
time to time throughout the chap-
ter, you will be asked to recall your
prior knowledge of multiplication of
polynomials.
The objective in factoring is to take a complicated polynomial and express
it as the product of simpler polynomial factors. You might ask, “Why would
you want to do this?” One practical answer is that, generally, you have fewer
restrictions on factors than you do on terms. Factors are joined by multipli-
cation, but terms are joined by addition or subtraction. The following prob-
lem illustrates this point.
Problem Follow the indicated directions for the six true sentences given
below. (For convenience, assume x and y are positive real numbers with x<y.)
- xy= xyx , but xy+≠y xy+.
The reality that factoring polynomials requires
agility in multiplying polynomials underscores
the importance of mastering previous skills in
mathematics before going on to new ones.
Expecting to learn a new math topic that relies
on previous skills that were not mastered is
a self-defeating strategy that often leads to
disappointing results. Some advice: Don’t make
this mistake!
