Answer
$[-5, 1] U [3, ∞)$
Work Step by Step
$x^3 + x^2 - 17x + 15 \geq 0$
Find the roots of the function
$x^3 + x^2 - 2x - 15x + 15$
$x (x^2 + x - 2) - 15(x-1)$
$x (x+2)(x-1) - 15(x-1)$
$(x-1)(x^2 + 2x -15)$
$(x+5)(x-1)(x-3)$
$x = -5, 1, 3$
Test numbers in between those zero values to determine if the function is negative or positive
(-∞, -5] $(-)(-)(-) = (-)$
[-5, 1] $(+)(-)(-) = (+)$
[1, 3] $(+)(+)(-) = (-)$
[3, ∞) $(+)(+)(+) = (+)$
Thus the solution is $[-5, 1] U [3, ∞)$