# Thread: [SOLVED] Factor or reverse FOIL help needed

1. ## [SOLVED] Factor or reverse FOIL help needed

3x^2-2x-1=0

2. Hi!

$\displaystyle 3x^{2}-2x-1$

You can solve $\displaystyle 3x^{2}-2x-1=0$, that is, find the roots of the polynomial. This can be done by using the quadratic formula:

$\displaystyle x^{2}+px+q=0 \mbox{ , Solution formula: } x = -\frac{p}{2}\pm \sqrt{(\frac{p}{2})^{2}-q}$

This will give you two roots. Call these roots a and b (assuming here that $\displaystyle a \neq b$ ). So you polynomial can be written

$\displaystyle (x-a)(x-b)$

We do the same with your polynomial:

$\displaystyle 3x^{2}-2x-1=0 \Longleftrightarrow x^{2}-\frac{2}{3}x-\frac{1}{3} =0$

Now using the quadratic formula we get: $\displaystyle x=\frac{2}{6} \pm \sqrt{\frac{4}{3}+\frac{1}{3}}$ , which gives the two solutions

$\displaystyle x = 1 \mbox{ and } x = -\frac{1}{3}$

So we can factor your polynomial as $\displaystyle 3(x-1)(x+\frac{1}{3})$ , and we multiply it out we indeed get what we started with.