SOLUTION: Solve the inequality. x^3+x^2 is less than or equal to 16x+16 Write your answer as an interval or union of intervals. If there is no real solution, click on "No solution".

Question 396999: Solve the inequality.
x^3+x^2 is less than or equal to 16x+16
Write your answer as an interval or union of intervals.
If there is no real solution, click on "No solution".
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
x^3+x^2 is less than or equal to 16x+16
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x^3+x^2-16x-16 < 0
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Find the zeroes because they are the boundaries
for the solution intervals.
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x = -1 is one of the zeroes.
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-1)....1....1....-16....-16
........1.....0.....-16....|..0
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The quotient is x^2-16
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So the other zeroes are +4 and -4
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Plot x = -4,-1, and 1 on a number line.
--
Test a value from each interval to find the solution set
for (x+1)(x-4)(x+4)<0
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If x = -10 you get -*-*- < 0; true so solutions in (-inf,-4)
If x = -2 you get -*-*+ < 0; false
If x = 0 you get +*-*+ < 0; true so solutions in (-1,1)
If x = 10 you get +*+*+ < 0; false
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Solution: (-inf,-4)U(-1,1)
=============================
Cheers,
Stan H.
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