Question

Pls help....

Solve the rational inequality and graph the solution set on a real number line. Express the solution set in interval notation :

x^3-2x^2-4x+8<0

Answer 1

(x^3 - 2x^2) - (4x - 8) < 0
x^2 (x-2) - 4(x-2) < 0
(x-2) (x^2-4) < 0
(x-2) (x-2) (x+2) < 0
(x-2)^2 (x+2) < 0

(x-2)^2 is always positive. So, (x+2) must be negative. I.e
x+2 < 0
x < -2

\[(-\infty,-2)\]

Answer 2

Great and thanks a million.