[SOLVED] Factor or reverse FOIL help needed

**JohnGalt** · June 24th 2009, 10:24 PM

3x^2-2x-1=0

I've completely forgotten how to factor more complex quadratic equations such as this. Please help. Thank you.

**Twig** · June 24th 2009, 11:18 PM

Hi!

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

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

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

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

$(x-a)(x-b)$

We do the same with your polynomial:

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

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

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

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

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