Question

In the given problem, solve and graph.

Express answers in both inequality and interval notaion.

$x^3>2x^2+x$

Answer 1

$x^3>2x^2+x$

$x^3-2x^2-x>0$

$x(x^2-2x-1)>0$

	x<$1-\sqrt{2}$	x=$1-\sqrt{2}$	$1-\sqrt{2}$<x<0	x=0	0<x<$1+\sqrt{2}$	x=$1+\sqrt{2}$	x>$1+\sqrt{2}$
x	-	-	-	0	+	+	+
x^2-2x-2	+	0	-	-	-	0	+
x(x^2-2x-2)	-	0	+	0	-	0	+

$\left[\begin{array}{cc}Solution:& 1-\sqrt{2}<x<0orx>1+\sqrt{2}\\ Decimal:& -0.41421\cdots <x<0orx>2.41421\dots \\ IntervalNotation:& (1-\sqrt{2},0)\cup (1+\sqrt{2},\infty )\end{array}\right]$