SOLUTION: I need help with this problem factoring it completely: -4x^2 + 23x - 28

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Question 258816: I need help with this problem factoring it completely:
-4x^2 + 23x - 28

Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!




First factor out a -1



Multiply the  by the 

Get 112.

Write down all the ways to break 112 into 2 factors of whole numbers

112x1
 56x2
 28x4
 16x7
 14x8

Notice that the last sign is a plus:



Plus means add so beside those numbers we
just multiplied, let's add them:

112x1  112+1=113
 56x2   56+2=58 
 28x4   28+4=32
 16x7   16+7=23
 14x8   14+8=22

Look at the middle term of



in absolute value.  It is a 23.  Now 
look among those sums we just found.  
Is there a 23 among them?  Yes.  That
means it can be factored. We find:

 16x7   16+7=23

So let's replace 23 by 



Now distribute it out



Factor 4x out of the first two terms:



Factor -7 out of the last two terms:



Notice the common factor 




Factor out the green 



We can now remove the outer parentheses but leave
the negative sign in front:



Edwin


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