SOLUTION: Factor completely -x^2+10x-21/-3x^2+23y-14

Question 232377: Factor completely
-x^2+10x-21/-3x^2+23y-14
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
Whenever you are factoring, keep an eye out for factoring out a -1. It can always be done and sometimes doing so makes a problem easier. Since factoring trinomials is easier with a positive leading coefficient, I am going to start by factoring out -1:

The trinomials are now easier to factor, especially the first one. The second one is a bit more difficult. Since 3 factors in only one way, 3 = 3*1, the factors will look like:
(3x )(x )
if it factors at all. And since the 14 is positive and the 23 is negative, the factors will look like:
(3x - )(x - )
Now we just have to figure out which factors of 14 (1 and 14 or 2 and 7) to use and where to place them in the above so that we would end up with 23 in the middle if you we to multiply.

Now we can cancel common factors:

leaving

(NOTE: Do not cancel the x's or the 3's here. They are not factors!)

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