Factor the binomial completely. Select "Prime" if the polynomial cannot be factored. \( t^{3}-36 t=\square \)

1. First, factor out the greatest common factor, which is \( t \): \[ t^{3} - 36t = t(t^2 - 36) \] 2. Notice that \( t^2 - 36 \) is a difference of squares since \( 36 = 6^2 \). The difference of squares factors as: \[ a^2 - b^2 = (a - b)(a + b) \] Here, \( a = t \) and \( b = 6 \), so: \[ t^2 - 36 = (t - 6)(t + 6) \] 3. Combine the factors to get the complete factorization: \[ t^{3}-36t = t(t - 6)(t + 6) \]