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Quadratic Expressions. Please tell me how to answer these questions fully. State...

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paulbarton | Honors

Posted October 18, 2012 at 11:46 PM via web

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Quadratic Expressions.

Please tell me how to answer these questions fully. State whether there is common factor or pattern. Then use decomposition.

D. 6a^2-7a+1

 

 

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lfryerda | High School Teacher | (Level 2) Educator

Posted October 19, 2012 at 12:46 AM (Answer #1)

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If you have more than one question, you need to make separate posts.

To factor using decomposition, you need to find the factors of the product of the first and last coefficient that add to the middle coefficient.

In this case, we are looking for factors of 6x1=6 that add to -7, which are -6 and -1.

Then split apart the middle term using these factors.  Finally, factor using group factoring twice.

`6a^2-7a+1`   split middle term

`=6a^2-6a-a+1`   factor by grouping

`=6a(a-1)-1(a-1)`   common factoring

`=(a-1)(6a-1)`

The expression factors into `(a-1)(6a-1)` .

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