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.
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