I need help with the first problem.

Factor.
100w^2 - 9

c^3 + 27
My approach: (c+3)(c+3)(c+3)
Is this correct?

The first expression is the difference of two squares, and factors into (10w + 3)(10w - 3)

The second is not correct, as you can verify by multiplying it out. c+3 is ONE factor, however. You can get the other factor by using synthetic division to compute (c^3+27)/(c+3)