Which method is the most efficient for factoring polynomials?

gillgill
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What is the fastest and easiest way to factor these?

ex. 3x^2+8x-3
 
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I started by looking for a root.
 
gillgill said:
What is the fastest and easiest way to factor these?

ex. 3x^2+8x-3

Remember, there are 3 usual methods for finding a quadratic root:
1) Quadratic Formula
2) Completing The Square
3) Factoring
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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