Kenneth M.

asked • 09/06/17

where did the 4x and the 1 come from?

12x2 +11x +2=0
12x2 +8x +3x+2=0
4x(3x+2) +1(3x+2)
(3x+2)(4x+1)

1 Expert Answer

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Philip P. answered • 09/06/17

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12x2 + 11x + 2 = 0
12x2 + 8x +3x + 2=0
 
Group:
 
     (12x2+ 8x) + (3x+2) = 0
 
Factor greatest common factor out of each group:
 
     4x(3x+2) + 1(3x+2) = 0
 
Factor out the (3x+2):
 
     (3x+2)(4x+1) = 0
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Kenneth M.

Where do the 4x and 1 come from????
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09/06/17

Philip P.

Basis rule for factoring out a greatest common factor:
 
(x·a + b·a) = a·(x+b)
 
Now (12x2 + 8x) = (4x·3x + 4x·2). Factor out the common factor, 4x:
 
(12x2 + 8x) = (4x·3x + 4x·2) = 4x(3x+2)
 
That's where the 4x comes from.  Now for the (3x+2) grouping the greatest common factor for 3x and 2 is 1:
 
(3x+2) = (3x·1 + 2·1) = 1·(3x+2)
 
That's where the 1 comes from:
 
(12x2+ 8x) + (3x+2) = 4x(3x+2) + 1(3x+2).
 
Now (3x+2) is the common factor, so factor it out leaving the 4x + 1 behind:
 
(3x+2)(4x+1)
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09/06/17

Kenneth M.

Thank you very much for explaining this to me, I needed that. I appreciate the help
 
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09/06/17

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