How do you solve x^3+4x^2>x+4x3+4x2>x+4 using a sign chart?

1 Answer
Steve M
Nov 30, 2016

-4 < x < -1 −4<x<−1
x > 1 x>1

Explanation:

x^3+4x^2 > x+4 x3+4x2>x+4
x^2(x+4) > x+4 x2(x+4)>x+4
x^2(x+4) - (x+4) > 0 x2(x+4)−(x+4)>0
(x^2-1)(x+4) > 0 (x2−1)(x+4)>0

We need to find the critical values (where a sign change can occur), which is given by (x^2-1)(x+4) = 0 (x2−1)(x+4)=0

Either x^2-1 = 0 => x =+-1x2−1=0⇒x=±1
or x+4 = 0 => x=-4 x+4=0⇒x=−4

So we need to examine the behaviour of (x^2-1)(x+4) in each of the intervals:

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Sign of (x^2-1)(x+4) = { ( (+)(-)<0,x < -4 ),( (+)(+)>0,-4 < x < -1 ),( (-)(+)<0,-1< x < 1 ),( (+)(+)>0,x > 1 ) :}

So the solution for (x^2-1)(x+4) > 0 is
-4 < x < -1 or x > 1

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