Find all values of such that . Answer with interval notation.

c³ + 4c > 5c²

Rearrange:  c³ - 5c²+ 4c > 0

Factor:   c(c² - 5c + 4) > 0          ----->         c(c - 4)(c - 1 ) > 0

Each section could either be positive or negative:

If all the factors are positive, the answer would be positive:  c > 0  and  c - 4 > 0  and  c - 1 > 0

           which is this:  c > 0  and  c > 4  and c > 1    which is true only when c > 4.

If two of the factors are positive, the answer will be negative, so we don't have to consider this.

If only one of the factors is positive, the answer will be negative; there are three possibilities:

          c > 0  and  c - 4 < 0  and  c - 1 < 0   --->   c > 0  and  c < 4  and  c < 1   --->   0 < c < 1

          c < 0  and c - 4 > 0  and  c - 1 < 0   --->   c < 0  and c > 4  and c < 1  (impossible)

          c < 0  and  c - 4 < 0  and  c - 1 > 0   --->  c < 0  and  c < 4  and  c > 1   (impossible)

If none of the factors is positive, the answer will be negative, so we don't have to consider this.

Answer:  Combining the first answer with the third answer:    {c > 4}  or  {0 < c < 1}