*25 POINTS* - Show your work. Factor all problems completely. (Greatest Common Factor)
1.) 12x^3 + 2x^2 - 30x - 5
2.) 63n^3 + 54n^2 = 105n - 90
3.) 25v^3 + 5v^2 + 30v + 6
4.) 96n^3 - 84n^2 + 112n - 98
5.) 4v^3 - 12v^2 - 5v + 15
6.) 24p^3 + 15p^2 - 56p - 35

Abottled water distributor wants to estimate the amount of water contained in 1-gallon bottles purchased from a nationally known water bottling company. the water bottling company’s specifications state that the standard deviation of the amount of water is equal to 0.02 gallon. a random sample of 50 bottles is selected, and the sample mean amount of water per 1-gallon bottle is 0.995 gallon a. construct a 99% confidence interval estimate for the popula-tion mean amount of water included in a 1-gallon bottle. b. on the basis of these results, do you think that the distributor has a right to complain to the water bottling company? why? c. must you assume that the population amount of water per bottle is normally distributed here? explain. d. construct a 95% confidence interval estimate. how does this change your answer to (b)?