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) About Me  (Show Source):
You can put this solution on YOUR website!


-4x%5E2+%2B+23x+-+28

First factor out a -1

-%28red%284%29x%5E2-23x%2Bred%2828%29%29

Multiply the red%284%29 by the red%2828%29

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:

%22-%28%224x%5E2-23xred%28%22%2B%22%2928%29

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

-%284x%5E2-red%2823%29x%2B28%29

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 red%28%2816%2B7%29%29

-%284x%5E2-red%28%2816%2B7%29%29x%2B28%29

Now distribute it out

-%284x%5E2-16x-7x%2B28%29

Factor 4x out of the first two terms:

-%284x%28x-4%29-7x%2B28%29

Factor -7 out of the last two terms:

-%284x%28x-4%29-7%28x-4%29%29

Notice the common factor green%28%28x-4%29%29%29


-%284x%2Agreen%28%28x-4%29%29-7%2Agreen%28%28x-4%29%29%29

Factor out the green green%28%28x-4%29%29

-%28green%28%28x-4%29%29%284x-7%29%29

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

-%28x-4%29%284x-7%29

Edwin