WHen I factor should I take out a GCF of 2x???(Speechless)

NVM i think it is alread simplified????

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- Jun 2nd 2009, 05:12 PMtiffieblahFActor 2x^2+2x-3
WHen I factor should I take out a GCF of 2x???(Speechless)

NVM i think it is alread simplified???? - Jun 2nd 2009, 05:37 PMDeadstar
Well it doesn't factor in the integers but it does in the reals.

If you take out 2x as a factor you get $\displaystyle 2x(x+1)-3$

If you set $\displaystyle 2x^2 + 2x - 3 = 0$ and use $\displaystyle \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ then you get factors in the real => $\displaystyle \bigg{(}x - \bigg{(}\frac{1}{2} - \sqrt{\frac{7}{4}}\bigg{)}\bigg{)}\bigg{(}x - \bigg{(}\frac{1}{2} + \sqrt{\frac{7}{4}}\bigg{)}\bigg{)}$.

Or alternatively you can notice that $\displaystyle x^2 + 2x - 3$ factorizes as $\displaystyle (x+3)(x-1)$ so you can factorize $\displaystyle 2x^2 + 2x - 3$ as $\displaystyle (x+3)(x-1) + x^2$