solve the following inequality. write the answer in interval notation

Question

x^3-4x^2-21x<0

please show work so i can understand this problem better! thanks

Answer 1

Since x^3-4x^2-21x = x(x+3)(x-7)

there are no repeated roots. So, at each root, the graph crosses the x-axis, and the function changes sign.

Starting with large negative x, all 3 factors are negative. So, on the number line, start with - signs and switch at each root:

----- -7 +++++ 0 ----- 3 +++++++

x is in (-oo,-7) U (0,3)