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: b^{3 }+ 49 b

Problem 2: a^{2 }+7ab + 10 b^{2}

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.

3a^{2 }-14a + 15

^{example }

Strategy for Factoring *ax*^{2} + *bx* + *c* by the *ac* Method

The *ac* method

Factor each trinomial.

a) |
2 |

b) |
2 |

c) |
10 |

Solution

a) |
In 2
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 7
Check by FOIL. |

b) |
In 2
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:
Only −3 and 4 have a sum of 1. Replace
Check by FOIL. |

c) |
Because
The only pair that has a sum of 13 is −2 and 15:
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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