solve the polynomial inequality and graph on number line. express in set interval rotation. Show work x^3 - 3x^2 - 9x + 27 < 0

Answer 1

x^3 - 3x^2 - 9x + 27 < 0
x^2(x-3) - 9(x-3) < 0
(x^2-9)(x-3) < 0
(x+3)(x-3)^2 < 0

Now, even without going through all the +/- combinations of factors, which can get tedious, you know that this curve crosses the x-axis at x = -3, and is tangent at x = +3.

So, it is only below the axis for x < -3.

Analyzing the factors, since (x+3)^2 is never negative, the function is negative only when (x+3) < 0. That is, for x < -3.