SOLUTION: Solve the following by factoring and making appropriate sign charts: {{{x^3+4x^2-x>=4}}} I'm not sure how to go about factoring this or what the appropriate sign charts are.

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Question 92804: Solve the following by factoring and making appropriate sign charts:

I'm not sure how to go about factoring this or what the appropriate sign charts are. If you could please show me the steps to this problem...I would appreciate it. Thank you! :)
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Solve the following by factoring and making appropriate sign charts:
x^3+4x^2-x>=4
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x^3+4x^2-x-4 >= 0
The coefficients add to zero so x=1 is a root
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Use synthetic division to find the factors other than x-1:
1)....1....4....-1....-4
........1....5....4...|..0
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Remainder is zero because 1 is a root.
Quotient is x^2+5x+4 which factors as (x+4)(x+1)
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Rewrite the Problem as follows:
(x+4)(x+1)(x-1) >= 0
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To satisfy the EQUALITY x may be -4, or -1, or 1
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Plot those three values on a number line.
They partition the number line into 4 intervals.
Check a test point in each interval to see where the solutions
for the INEQUALITY (x+4)(x+1)(x-1) > 0 are
In (-inf,-4) select x=-5; You get -1*-4*-6 <0 so no solutions here
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In (-4,-1) select x=-2; you get 2*-1*-3 >0 so solutions in that interval
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In (-1,1) select x = 0; you get 4*1*-1 <0 so no solution here
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In (1,inf) select x=2; you get 6*3*1>0 so solution in that interval
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Final Solution:
[-4,-1]U[1,inf}
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Cheers,
Stan H.