Factor completely. 9t^3-2t^2+18t-4 square

To factor the polynomial \(9t^3 - 2t^2 + 18t - 4\) completely, we can follow these steps:<br /><br />1. **Group the terms**: Group the polynomial into two pairs.<br /> \[<br /> (9t^3 - 2t^2) + (18t - 4)<br /> \]<br /><br />2. **Factor out the greatest common factor (GCF) from each group**:<br /> \[<br /> t^2(9t - 2) + 2(9t - 2)<br /> \]<br /><br />3. **Factor by grouping**: Notice that both groups contain a common binomial factor \((9t - 2)\).<br /> \[<br /> (9t - 2)(t^2 + 2)<br /> \]<br /><br />So, the completely factored form of the polynomial \(9t^3 - 2t^2 + 18t - 4\) is:<br />\[<br />(9t - 2)(t^2 + 2)<br />\]