FActor 2x^2+2x-3

**tiffieblah** · June 2nd 2009, 05:12 PM

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

NVM i think it is alread simplified????

**Deadstar** · June 2nd 2009, 05:37 PM

Well it doesn't factor in the integers but it does in the reals.
If you take out 2x as a factor you get $2x(x+1)-3$

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

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

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