Question

In the given problem, solve and graph. Express the answer in both inequality and interval notation. $x^3+2x^2\le 8x$

Answer 1

$x^3+2x^2\le 8x$

$x^3+2x^2-8x\le 0$

$x(x-2)(x+4)\le 0$

	x<-4	x=- 4	- 4<x<0	x=0	0<x<2	x=2	x>2
x-2	-	-	-	-	-	0	+
x	-	-	-	0	+	+	+
x+4	-	0	+	+	+	+	+
x(x-2)(x+4)	-	0	+	0	-	0	+

$\left[\begin{array}{cc}Solution:& x\le -4or0\le x\le 2\\ IntervalNotation:& (-\infty ,-4]\cup [0,2]\end{array}\right]$