document.write( "Question 893866: What factors of -6 add up to -16?
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Algebra.Com's Answer #541593 by richwmiller(17219) $\"\"$ $\"About$

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x^2-16-6=0
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Solved by pluggable solver: Factoring using the AC method (Factor by Grouping)

Looking at the expression $\"x%5E2-16x-6\"$ , we can see that the first coefficient is $\"1\"$ , the second coefficient is $\"-16\"$ , and the last term is $\"-6\"$ .

Now multiply the first coefficient $\"1\"$ by the last term $\"-6\"$ to get $\"%281%29%28-6%29=-6\"$ .

Now the question is: what two whole numbers multiply to $\"-6\"$ (the previous product) and add to the second coefficient $\"-16\"$ ?

To find these two numbers, we need to list all of the factors of $\"-6\"$ (the previous product).

Factors of $\"-6\"$ :

1,2,3,6

-1,-2,-3,-6

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

These factors pair up and multiply to $\"-6\"$ .

1*(-6) = -6
2*(-3) = -6
(-1)*(6) = -6
(-2)*(3) = -6

Now let's add up each pair of factors to see if one pair adds to the middle coefficient $\"-16\"$ :

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First Number	Second Number	Sum
1	-6	1+(-6)=-5
2	-3	2+(-3)=-1
-1	6	-1+6=5
-2	3	-2+3=1

From the table, we can see that there are no pairs of numbers which add to $\"-16\"$ . So $\"x%5E2-16x-6\"$ cannot be factored.

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Answer:

So $\"x%5E2-16%2Ax-6\"$ doesn't factor at all (over the rational numbers).

So $\"x%5E2-16%2Ax-6\"$ is prime.

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