Question

Express the solution of, x^3 + 2x^2 < x + 2, using interval notation.

Answer 1

x³ + 2x² - x - 2 < 0

x³ - x + 2x² - 2 < 0

x(x² - 1) - 2(x² - 1) < 0

(x - 2)(x² - 1) < 0

(x - 2)(x - 1)(x + 1) < 0

by chacking we get the solution

x ∈ (-∞,-1) ∪ (-1,1)