Factor 360t + 10t ^3 - 120t ^2.
10t(t - 6)(t + 6)
10t(t - 6)^2
-10t(t - 6)(t + 6)

The answer is:  [B]:  " 10t (t - 6)² "

Note:


Choice [A]:  10t(t - 6)(t + 6) = 10t (t² - 36) = 10t³ - 360t .

Choice [C]:  is similar; except with "-10t" in lieu of "10t" :
 
   -10t (t-6)(t+6) =  -10t (t² -36) =  -10t³ + 360t ;

This leaves us with the remaining answer choice:

Answer choice:  [B]:  " 10t (t - 6)² " .


But let us check:

(t - 6)² = (t - 6)(t - 6) = t² - 6t - 6t + 36 = t² - 12t + 36 ;

10t (t² - 12t + 36) =  10t³ - 120t² + 360t ;

which equals the value presented in the question:

which is:   360t + 10t³ - 120t² "

Note:  "our solved value:  " 10t³ - 120t² + 360t "  = ? 
   (the value in the question:  " 360t + 10t³ - 120t² " ?

360t + 10t³ - 120t² =? 10t³ - 120t² + 360t ??
           
                              = +360t +10t³ - 120t² ??  YES!

The answer is:  [B]:  " 10t (t - 6)² " .