Factor completely. \[ 1+30 s^{3}-5 s-6 s^{2} \]

To factor the expression \( 1 + 30s^3 - 5s - 6s^2 \), first, let's rearrange it for easier manipulation: \[ 30s^3 - 6s^2 - 5s + 1. \] Next, we can group the terms: \[ (30s^3 - 6s^2) + (-5s + 1). \] Now, factor out the common factors from each group: \[ 6s^2(5s - 1) - 1(5s - 1). \] Notice that \( (5s - 1) \) is a common factor: \[ (5s - 1)(6s^2 - 1). \] The term \( 6s^2 - 1 \) can be further factored using the difference of squares: \[ 6s^2 - 1 = \sqrt{6} \cdot s - 1)(\sqrt{6} \cdot s + 1).\] Thus, the complete factored form of the expression is: \[ (5s - 1)(\sqrt{6} \cdot s - 1)(\sqrt{6} \cdot s + 1). \]