SOLUTION: How will you factor x squared minus 12x minus 5?

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Question 870601: How will you factor x squared minus 12x minus 5?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

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


Now multiply the first coefficient 1 by the last term -5 to get %281%29%28-5%29=-5.


Now the question is: what two whole numbers multiply to -5 (the previous product) and add to the second coefficient -12?


To find these two numbers, we need to list all of the factors of -5 (the previous product).


Factors of -5:
1,5
-1,-5


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


These factors pair up and multiply to -5.
1*(-5) = -5
(-1)*(5) = -5

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


First NumberSecond NumberSum
1-51+(-5)=-4
-15-1+5=4



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


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Answer:


So x%5E2-12x-5 doesn't factor at all (over the rational numbers).


So x%5E2-12x-5 is prime.


If you want to solve x%5E2-12x-5=0, you have to either complete the square or use the quadratic formula.