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2.01 Review of Factoring Intermediate Algebra: One Step at a Time. Pages 139 - 142: #33, 37, 51, 52, 56Dr. Robert J. Rapalje Seminole State College of Florida Sanford, FL 32773
To see Section 2.01, with explanations, examples, exercises, and answers, click here!
p.
140. #33.
Next, notice that this is a SUM of two cubes!
The FIRST is
What you have is:
p.
141. #37.
The first step in any factoring problem should be to take out the common
factor. In this case the common factor is
Next, notice that this is a SUM of two cubes! The FIRST is
What you have is:
p. 142. # 51.
Solution:
This is a grouping
problem in which it works to group the first two terms together and the
second two term together. From the first two terms you can take out a
common factor of
Now there is a common factor of
Next, factor the difference of two squares:
And again, the difference of two squares:
p. 142. # 52.
Solution: You may have guessed from the grouping by parentheses and by the colors used in this problem, that it is a trinomial. Factor the first grouping as a trinomial, then factor the middle two terms by taking out a common factor of 4, and leave the last 4 alone:
Now, the entire problem is a trinomial, which factors: It looks nicer if you clean it up:
And even better, you can write it like this:
p. 142. # 56.
Solution:
This is a grouping
problem in which it works to group the first two terms together and the
second two term together. From the first two terms you can take out a
common factor of
Now there is a common factor of
Next, factor the difference of two squares:
And again, the difference of two squares:
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