Project #51178 - Factoring

For the problems 1 and 2 factor the polynomials using whatever strategy seems appropriate State what methods you will use and then demonstrate the methods on your problems, explaining the process as you go. Discuss any particular challenges those particular polynomials posed for the factoring.

Problem 1:  b3 + 49 b

Problem 2:  a2 +7ab + 10 b2

 

Part 2: make sure you use the “ac method” regardless of what the book’s directions say. Show the steps of this method in your work in a similar manner as how the book shows it in examples.

3a2 -14a + 15

example  

Strategy for Factoring ax2 + bx + c by the ac Method

The ac method

Factor each trinomial.

a)

2x2 + 7x + 6

b)

2x2 + x − 6

c)

10x2 + 13x − 3

Solution

a)

In 2x2 + 7x + 6 we have a = 2, b = 7, and c = 6. So,

http://www.aleks.com/alekscgi/x/Isl.exe/1o_u-IgNsIkasNW8D8A9PVVfSsFqwXz0aYw2fRUtCOD8KLuM85QXm3RVDlDYpNgLyzbMLlDgzR-bwHQzyU79qO0wexxQAytRn-e2DRdZnp4VmtUhq/path/aleks/ebook/figures/0077486129/exch05_13.png

Now we need two integers with a product of 12 and a sum of 7. The pairs of integers with a product of 12 are 1 and 12, 2 and 6, and 3 and 4. Only 3 and 4 have a sum of 7. Replace 7x by 3x + 4x and factor by grouping:

http://www.aleks.com/alekscgi/x/Isl.exe/1o_u-IgNsIkasNW8D8A9PVVfSsFqwXz0aYw2fRUtCOD8KLuM85QXm3RVDlDYpNgLyzbMLlDgzR-bwHQzyU79qO0wexxQAytRn-e2DRdZnp4VmtUhq/path/aleks/ebook/figures/0077486129/dug_05_4356_pp348_001.png

Check by FOIL.

b)

In 2x2 + x − 6 we have a = 2, b = 1, and c = −6. So,

http://www.aleks.com/alekscgi/x/Isl.exe/1o_u-IgNsIkasNW8D8A9PVVfSsFqwXz0aYw2fRUtCOD8KLuM85QXm3RVDlDYpNgLyzbMLlDgzR-bwHQzyU79qO0wexxQAytRn-e2DRdZnp4VmtUhq/path/aleks/ebook/figures/0077486129/exch05_14.png

Now we need two integers with a product of −12 and a sum of 1. We can list the possible pairs of integers with a product of −12 as follows:

http://www.aleks.com/alekscgi/x/Isl.exe/1o_u-IgNsIkasNW8D8A9PVVfSsFqwXz0aYw2fRUtCOD8KLuM85QXm3RVDlDYpNgLyzbMLlDgzR-bwHQzyU79qO0wexxQAytRn-e2DRdZnp4VmtUhq/path/aleks/ebook/figures/0077486129/dug_05_4356_pp348_002.png

Only −3 and 4 have a sum of 1. Replace x by −3x + 4x and factor by grouping:

http://www.aleks.com/alekscgi/x/Isl.exe/1o_u-IgNsIkasNW8D8A9PVVfSsFqwXz0aYw2fRUtCOD8KLuM85QXm3RVDlDYpNgLyzbMLlDgzR-bwHQzyU79qO0wexxQAytRn-e2DRdZnp4VmtUhq/path/aleks/ebook/figures/0077486129/dug_05_4356_pp348_001.png

Check by FOIL.

c)

Because ac = 10(−3) = −30, we need two integers with a product of −30 and a sum of 13. The product is negative, so the integers must have opposite signs. We can list all pairs of factors of −30 as follows:

http://www.aleks.com/alekscgi/x/Isl.exe/1o_u-IgNsIkasNW8D8A9PVVfSsFqwXz0aYw2fRUtCOD8KLuM85QXm3RVDlDYpNgLyzbMLlDgzR-bwHQzyU79qO0wexxQAytRn-e2DRdZnp4VmtUhq/path/aleks/ebook/figures/0077486129/dug_05_4356_pp348_004.png

The only pair that has a sum of 13 is −2 and 15:

http://www.aleks.com/alekscgi/x/Isl.exe/1o_u-IgNsIkasNW8D8A9PVVfSsFqwXz0aYw2fRUtCOD8KLuM85QXm3RVDlDYpNgLyzbMLlDgzR-bwHQzyU79qO0wexxQAytRn-e2DRdZnp4VmtUhq/path/aleks/ebook/figures/0077486129/dug_05_4356_pp348_003.png

Check by FOIL.

 

  • Incorporate the following five math vocabulary words into your discussion. Use bold font to emphasize the words in your writing (Do not write definitions for the words; use them appropriately in sentences describing your math work.):
    • Factor  
    • GCF  
    • Prime factors  
    • Perfect square 
    • Grouping

Your initial post should be 150-250 words in length

Subject Mathematics
Due By (Pacific Time) 12/18/2014 07:00 am
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