Factor completely. 40u^3-50u^2-4u+5 square

To factor the polynomial \(40u^3 - 50u^2 - 4u + 5\) completely, we can follow these steps:<br /><br />1. **Group the terms**:<br /> \[<br /> (40u^3 - 50u^2) + (-4u + 5)<br /> \]<br /><br />2. **Factor out the greatest common factor (GCF) from each group**:<br /> \[<br /> 10u^2(4u - 5) - 1(4u - 5)<br /> \]<br /><br />3. **Factor by grouping**:<br /> Notice that \((4u - 5)\) is a common factor in both groups:<br /> \[<br /> (10u^2 - 1)(4u - 5)<br /> \]<br /><br />4. **Factor the difference of squares**:<br /> The term \(10u^2 - 1\) is a difference of squares, which can be factored as:<br /> \[<br /> 10u^2 - 1 = ( \sqrt{10}u - 1)( \sqrt{10}u + 1)<br /> \]<br /><br />5. **Combine all factors**:<br /> \[<br /> ( \sqrt{10}u - 1)( \sqrt{10}u + 1)(4u - 5)<br /> \]<br /><br />So, the completely factored form of the polynomial \(40u^3 - 50u^2 - 4u + 5\) is:<br />\[<br />( \sqrt{10}u - 1)( \sqrt{10}u + 1)(4u - 5)<br />\]