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How do you factor t^2 (3t^2 + 2)/2t ?

The answer that I got was t(3t^2 + 2) / 2 but the answer stated was t((3/2)t^2 + 1). 
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2 Answers

The 2 answers are equal.  You got
 
t (3t2 + 2) / 2
 
Distribute the 1/2 and get
 
t (3t2 + 2) / 2 = t [(3/2)t2 + 2/2] = t [(3/2)t2 + 1]
 
This gives the stated answer.  They are equal; it is just a matter of distributing the 1/2.
It is the same thing:
 
t^2(3t^2 +2)/(2t) = t(3t^2 + 2)/2 = 1/2 ( t(3t^2 + 2)) = t(3/2t^2 + 1)