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# Polynomial Inequalities

Solving polynomial inequalities requires that we divide the polynomial into discrete intervals.

For example, if we have $$x^2 +6x - 16 > 0$$, we can first find the places where the expression is equal to 0. Factoring, we can see that $$(x+8)(x-2) = x^2 +6x -16$$, so the polynomial is equal to 0 at $$x = -8$$ and at $$x = 2$$. This means that on the intervals $$(-\infty, -8), (-8,2),$$ and $$(2, \infty)$$, the expression will either be only $$>0$$ or $$< 0$$ (because it can't pass through zero on those intervals). Testing each interval, we find that the expression is positive on the outer intervals and is negative on $$(-8,2)$$.

Thus the solution is $$x < -8$$ and $$x > 2$$.

Note by Arron Kau
3 years, 2 months ago