1. ## trinomial

18s^2-12st-30t^2

2. ## factor out 6

$\displaystyle 18s^2-12st-30t^2$

factor out 6

$\displaystyle 6\left(3s^2 - 2st - 5t^2\right)$

you may want to see if this was copied ok

3. Originally Posted by taemonique
18s^2-12st-30t^2

$\displaystyle 18s^2 - 12st - 30 t^2$

$\displaystyle 6(3s^2 - 2st - 5 t^2 )$

consider t is a constant try to guess it we need two numbers when we multiply them we get -15 and when add then we get -2 (-5,3)

$\displaystyle 6(3s -5t)(s+t)$

or

$\displaystyle 18\left(s^2 -\frac{2}{3} \cdot st - \frac{5}{3} \cdot t^2 \right)$

treat t like a constant and use the general law

$\displaystyle s = \frac{-(-2t) \mp \sqrt{4t^2 - 4(3)(-5t^2)}}{6}$

$\displaystyle s= \frac{2t \mp \sqrt{4(16)t^2}}{6}$

$\displaystyle s = \frac{2t \mp 8t }{6}$

so

$\displaystyle s= \frac{5}{3} t$ or $\displaystyle \;\; s = -t$

$\displaystyle 18\left(s^2 -\frac{2}{3} \cdot st - \frac{5}{3} \cdot t^2 \right)$

$\displaystyle 18\left(s - \frac{5t}{3} \right)\left(s +t\right)$