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I need some help factoring: $6-4x-12$.

How do I solve this problem?

Aren’t I supposed to take out the GCF, which is $2$?

This is how I solved it: $2 (3-2x-6)$. When I simplified this expression, it keeps going back to $6 - 4x - 12$.

Ocean
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  • First note that $6-4x-12=-4x-6$. I'd factor that as $-2(2x-3)$ – Hagen von Eitzen Dec 15 '19 at 21:06
  • How’d you get negative -2? The GCF of 6,4, and 12 is 2! – Ocean Dec 15 '19 at 21:07
  • First add the $6$ to the $-12$ to get $-6$ so $6-4x - 12 = -4x -6$. – fleablood Dec 15 '19 at 21:11
  • "When I simplified this expression, it keeps going back" Why does that surprise you? If by "simplify" you mean multiply the terms out, then you WANT to get the same thing back. If you got something different then you did something wrong because all of these expressions should just be different expressions for the same value. – fleablood Dec 15 '19 at 21:14
  • $\begin{array}\ 6 - 4x -12 = \ -4x -6=\-(4x + 6)=\ -2(2x + 3)\end{array}$ – fleablood Dec 15 '19 at 21:17
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    @fleablood perhaps you should post your comments as an answer? –  Dec 15 '19 at 21:20
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    @Ocean Sorry, that should have been $2(-2x-3)$ or (preferred by me) $-2(2x+3)$. I think it looks nicer with a leading negative sign instead of many negative signs sprinkled into the other factor. – Hagen von Eitzen Dec 15 '19 at 21:57

2 Answers2

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Note that $6-12=-6$. Thus $6-4x-12$ is the same as $-4x-6$. The common factor here is $-2$, so one gets $-2(2x+3)$ as the final result.

clathratus
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If you want to get the same answer as the comments without starting over note $-6+3=-3$ which makes what you have $2(-2x-3)$ then factor the -1 out to get $(-1)2(2x+3)=-2(2x+3)$