SOLUTION: factor completely {{{2x^2-24x-14}}}

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Question 892659: factor completely
2x%5E2-24x-14
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

2x%5E2-24x-14 Start with the given expression.


2%28x%5E2-12x-7%29 Factor out the GCF 2.


Now let's try to factor the inner expression x%5E2-12x-7


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Looking at the expression x%5E2-12x-7, we can see that the first coefficient is 1, the second coefficient is -12, and the last term is -7.


Now multiply the first coefficient 1 by the last term -7 to get %281%29%28-7%29=-7.


Now the question is: what two whole numbers multiply to -7 (the previous product) and add to the second coefficient -12?


To find these two numbers, we need to list all of the factors of -7 (the previous product).


Factors of -7:
1,7
-1,-7


Note: list the negative of each factor. This will allow us to find all possible combinations.


These factors pair up and multiply to -7.
1*(-7) = -7
(-1)*(7) = -7

Now let's add up each pair of factors to see if one pair adds to the middle coefficient -12:


First NumberSecond NumberSum
1-71+(-7)=-6
-17-1+7=6



From the table, we can see that there are no pairs of numbers which add to -12. So x%5E2-12x-7 cannot be factored.


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Answer:


So 2x%5E2-24x-14 simply factors to 2%28x%5E2-12x-7%29


In other words, 2x%5E2-24x-14=2%28x%5E2-12x-7%29.