6(t^2 + 12) How do I tell if this is factored completely?

Question

How do I tell if this is factored completely?  If it's not factored completely, how do I factor it?

Answer 1

Another way is to look at each element inside the parentheses. In this case, t^2 and 12 are the two elements. You ask yourself, "Do these two elements share a common factor?" If the answer is yes, then you have not completely factored the expression, but if the answer is no, then you have. In this case, t^2 and 12 do not share a common factor, so you have completely factored the expression. 

Answer 2

One way is to use the discriminant from the quadratic equation. The discriminant is b² - 4ac (what is under the radical)

If it's positive, there are two real roots. 
If it's zero, there is a o double root. 
If it's negative, there are complex roots. 

Plugging values in (since there is no linear term, b = 0) we get 
0² - 4(1)(12) = -48

Since it's negative, there are complex roots. So the problem is factored completely.