Download M0370 Written HW 5A

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Elementary Algebra Written Homework
Chapter 5 Part A
Managing large numbers in the Grouping Method for Trinomials [5.3]
Consider the following example.
18x 2 +131x ! 30
ac = !540
b = 131
Does it look intimidating to list all factor pairs of -540? Try this approach. Start with the prime factorization of
540. For our purposes, we will not use exponential notation.
540 = 2 ! 2 !3!3!3! 5
All factor pairs of 540 come from a grouping of these factors. For example:
540 = ( 2 ! 2 !3) ! (3!3! 5)
540 = (12 ) ! ( 45)
Of course, it is usually necessary to change the order of the factors to get a grouping that works. For this
problem, the following grouping gives us a pair of factors that work.
540 = ( 2 ! 2 ) ! (3!3!3! 5)
540 = ( 4 ) ! (135)
Now we are ready to factor this seemingly quite daunting polynomial using the grouping method.
18x 2 +131x ! 30
18x 2 ! 4x +135x ! 30
2x ( 9x ! 2 ) + 5 ( 9x ! 2 )
(2x + 5) (9x ! 2 )
1. Factor 36x ! 27x ! 28 using the Grouping Method.
2
Ch 5A
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Factoring completely [5.5]
Multiplying your factors is a good way to catch some errors, but it will not help you check to see if you have
factored completely. Don’t forget to look for a GCF in the first step, or to notice a pattern like difference of
squares in your answer, which can be factored further.
2.
(x
3.
(x
2
2
)
! 5x ( x ! 3) is not the complete factorization of x 3 ! 8x 2 + 15x . Explain why not.
+ 4 ) ( x 2 ! 4 ) is not the complete factorization of x 4 !16 . Explain why not.
Develop a Factoring Strategy [5.5]
It is important to follow a factoring strategy. Don’t start each factoring problem by drawing sets of parentheses
and trying to figure it out from scratch. Instead, carefully read section 5.5 so that you learn how to recognize
the different factoring patterns that arise.
4. What is the first step in any factoring problem?
5. The second step in a factoring problem is to classify the polynomial by number of terms. Describe what you
would try for each of the following:
a. two terms
b. three terms
c. four terms
6. What can you do to help ensure that you have factored completely?
7. Finally, check a factorization by doing what?
Ch 5A
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