Question

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

Factor by grouping.

Answer 2

first solve
\[\large x^3-3x^2-9x+27=0 \]

Answer 3

x = 3?

Answer 4

x³-3x²-9x+27<0
Factor:
(x+3)(x²-6x+9)<0
(x+3)(x-3)²<0
The zeroes of the cubic are -3 and 3.
(x-3)² cannot be negative because it's a square.
So the cubic is negative when x+3<0 that's when x<-3.
In interval notation that's (-∞,-3).

Answer 5

@helder_edwin