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

Question

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

Answer 1

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.

Answer 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)