College Algebra
Answer/Discussion to Practice Problems
Tutorial 7: Factoring Polynomials
Answer/Discussion
to 1a

The first thing that we always check when we are factoring is WHAT?
The GCF. In this case, there is one.
Factoring out the GCF of x we get: 

*Factor an x out
of every term

Next, we assess to see if there is anything else that we can factor.
This fits the form of the difference
of two squares. So we will factor using that rule: 

*Fits the form of a diff. of two squares
*Factor as the prod. of sum and diff. of bases

Note that if we would multiply this out and the original expression
out we would get the same polynomial. 
Answer/Discussion
to 1b

The first thing that we always check when we are factoring is WHAT?
The GCF. In this case, there is not one.
So we assess what we have. This is a trinomial that does not fit the
form of a perfect square trinomial. Looks like we will have to use trial
and error: 

*Factor by trial and error

There is no more factoring that we can do in this problem.
Note that if we would multiply this out, we would get the original polynomial. 
Answer/Discussion
to 1c

The first thing that we always check when we are factoring is WHAT?
The GCF. In this case, there is not one.
So we assess what we have. This is a polynomial with four terms.
Looks like we will have to try factoring
it by grouping: 

*Group in two's
*Factor out the GCF out of each separate (
)
*Factor out the GCF of (x
 y)

There is no more factoring that we can do in this problem.
Note that if we would multiply this out, we would get the original polynomial. 
Answer/Discussion
to 1d

Since this is a SUM of two squares it DOES NOT factor.
That means this polynomial is prime. 
Answer/Discussion
to 1e

The first thing that we always check when we are factoring is WHAT?
The GCF. In this case, there is one.
Factoring out the GCF of x we get: 

*Factor a 2 out
of every term

Next, we assess to see if there is anything else that we can factor.
This fits the form of the difference
of two cubes. So we will factor using that rule: 

*Fits the form of a diff. of two cubes
*Binomial is diff. of bases
*Trinomial is 1st base squared, plus prod.
of bases, plus 2nd base squared 
There is no more factoring that we can do in this problem.
Note that if we would multiply this out, we would get the original polynomial. 
Answer/Discussion
to 1f

The first thing that we always check when we are factoring is WHAT?
The GCF. In this case, there is one.
Factoring out the GCF of x we get: 

*Factor a 4 out
of every term

Next, we assess to see if there is anything else that we can factor.
This fits the form of the perfect
square trinomial. So we will factor using that rule: 

*Fits the form of a perfect sq. trinomial
*Factor as the diff. of bases squared 
There is no more factoring that we can do in this problem.
Note that if we would multiply this out, we would get the original polynomial. 
Last revised on Dec. 13, 2009 by Kim Seward.
All contents copyright (C) 2002  2010, WTAMU and Kim Seward. All rights reserved.

