J) Factor completely. 2s^3+4s^2+s+2 square

To factor the polynomial \(2s^3 + 4s^2 + s + 2\) completely, we can follow these steps:<br /><br />1. **Group the terms**: Group the polynomial into pairs to facilitate factoring by grouping.<br /> \[<br /> 2s^3 + 4s^2 + s + 2 = (2s^3 + 4s^2) + (s + 2)<br /> \]<br /><br />2. **Factor out the greatest common factor (GCF) from each group**:<br /> \[<br /> 2s^2(s + 2) + 1(s + 2)<br /> \]<br /><br />3. **Factor out the common binomial factor**:<br /> \[<br /> (2s^2 + 1)(s + 2)<br /> \]<br /><br />So, the completely factored form of the polynomial \(2s^3 + 4s^2 + s + 2\) is:<br />\[<br />(2s^2 + 1)(s + 2)<br />\]