SOLUTION: I keep trying on this problem and I'm running out of time and sanity. Please for the love of God, help me. x5+24>3x3+8x2. I can't even figure out how to write it on the computer

Algebra ->  Algebra  -> Inequalities -> SOLUTION: I keep trying on this problem and I'm running out of time and sanity. Please for the love of God, help me. x5+24>3x3+8x2. I can't even figure out how to write it on the computer      Log On

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Question 78550: I keep trying on this problem and I'm running out of time and sanity. Please for the love of God, help me. x5+24>3x3+8x2. I can't even figure out how to write it on the computer. That should be x to the power of 5, plus 24 > 3x to the power of 3 plus 8x squared. I understand that you need to bring everything over to equal 0. I have found one factor of it too, (x-2) but can't completely solve. Thanks so much!
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E5%2B24%3E3x%5E3%2B8x%5E2
x%5E5-3x%5E3-8x%5E2%2B24%3E0 Get all terms to one side
x%5E3%28x%5E2-3%29-8%28x%5E2-3%29%3E0 Factor out the GCF
%28x%5E3-8%29%28x%5E2-3%29%3E0 Combine like terms
%28x%5E3-8%29%28x%5E2-3%29=0 Now make an equation
Set each factor equal to zero
x%5E3-8=0
%28x-2%29%28x%5E2%2B2x%2B4%29=0 use the difference of cubes
Set x-2 equal to zero
x-2=0
x=2
Set x%5E2%2B2x%2B4 equal to zero
x%5E2%2B2x%2B4=0
This cannot be factored further

Now set x%5E2-3 equal to zero
x%5E2-3=0
x%5E2=3
x=0%2B-sqrt%283%29
So we have
x=sqrt%283%29 or x=-sqrt%283%29 or x=2
These are the points where x%5E5-3x%5E3-8x%5E2%2B24 goes through the x-axis. These are the turning points from positive to negative or vice versa. In other words, at these points the graph will change from f%28x%29%3E0 to f%28x%29%3C0 or vice versa. So lets graph the equation y=x%5E5-3x%5E3-8x%5E2%2B24
+graph%28+300%2C+200%2C+-6%2C+5%2C+-10%2C+10%2Cx%5E5-3x%5E3-8x%5E2%2B24%29+
From the graph we can see that f%28x%29%3E0 in the interval
[-sqrt%283%29, sqrt%283%29] U [2,)