Factor completely. 10k^3+5k^2-16k-8 square

To factor the polynomial \(10k^3 + 5k^2 - 16k - 8\) completely, we can follow these steps:<br /><br />1. **Group the terms**: Group the polynomial into two pairs.<br /> \[<br /> (10k^3 + 5k^2) + (-16k - 8)<br /> \]<br /><br />2. **Factor out the greatest common factor (GCF) from each group**:<br /> \[<br /> 5k^2(2k + 1) - 8(2k + 1)<br /> \]<br /><br />3. **Factor by grouping**: Notice that \((2k + 1)\) is a common factor.<br /> \[<br /> (5k^2 - 8)(2k + 1)<br /> \]<br /><br />4. **Factor the quadratic term if possible**: The quadratic \(5k^2 - 8\) does not factor nicely over the integers, so we leave it as is.<br /><br />Thus, the completely factored form of the polynomial \(10k^3 + 5k^2 - 16k - 8\) is:<br />\[<br />(5k^2 - 8)(2k + 1)<br />\]