Need help with Factoring a polynomial please.
3x^2+7x+2, my answer (3x+1)(2x+1) but I'm not sure it could be (3x+1)(x+2). thanks for taking time to look it over.
Hello,
use completing the square to factor this sum:
$\displaystyle 3x^2+7x+2 = 3\left(x^2 + \frac{7}{3}x+\frac{2}{3} \right) $ = $\displaystyle 3\left( \left(x^2 + \frac{7}{3}x+\frac{49}{36}\right) - \frac{49}{36} +\frac{2}{3} \right) = 3\left( \left(x + \frac{7}{6}\right)^2 - \frac{25}{36} \right)$ = $\displaystyle 3\left( \left(x + \frac{7}{6}\right)^2 - \left(\frac{5}{6} \right)^2 \right)$
As you can see you've got a difference of squares which can be factored easily:
$\displaystyle 3\left( \left(x + \frac{7}{6}\right)^2 - \left(\frac{5}{6} \right)^2 \right) = 3\left( x + \frac{7}{6}+ \frac{5}{6} \right) \left( x + \frac{7}{6} - \frac{5}{6} \right)$
Collect the fractions and multiply the 2nd bracket by the factor 3:
$\displaystyle (x+2)(3x+1)$
A personal remark: I know there exist formulae which will give you the result directly and immediately. But they use the way I've demonstrated too - you only can't see it at once.