Final answer:
To factor completely -6u⁶-14u⁵+6u⁴+14u³, we can first look for common factors. Then, we can factor by grouping to simplify the expression. The completely factored form of the expression is 2u³(3u + 7)(-u² + 3).
Step-by-step explanation:
To factor completely -6u⁶-14u⁵+6u⁴+14u³, we can first look for common factors. In this case, each term has a common factor of 2u³. So, we can factor out 2u³ to get: 2u³(-3u³ - 7u² + 3u + 7). Now, we can factor the remaining expression by grouping. Group the first two terms and the last two terms separately: 2u³(-3u³ - 7u²) + 2u³(3u + 7). Factor out the common factor from each group: 2u³(-u²(3u + 7) + 3(3u + 7)). Now, we see that we have a common factor of (3u + 7) in both terms. Factor it out: 2u³(3u + 7)(-u² + 3). Therefore, the completely factored form of -6u⁶-14u⁵+6u⁴+14u³ is 2u³(3u + 7)(-u² + 3).