Chapter 3 - Section 3.7 - Polynomial and Rational Inequalities - 3.7 Exercises - Page 316: 10

$(-3, 1)$

$x^4 + 3x^3 < x + 3$ Find the roots of the function $x^4 + 3x^3 - x - 3 < 0$ $x^3(x +3) - 1 (x+3)$ $(x^3 - 1) (x+3)$ $x = -3, 1$ Test numbers in between those zero values to determine if the function is negative or positive (-∞, -3) $(-)(-) = (+)$ (-3, 1) $(-)(+) = (-)$ (1, ∞) $(+)(+) = (+)$ Thus the solution is $(-3, 1)$