Question
Asked Dec 12, 2019
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Solve the following inequalities by the most convenient method. Please show all work. Write thesolution set in interval notation.

x3 + 4x2 - 9x - 36 ≥ 0
 

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Expert Answer

Step 1

Factor x^3+4x^2-9x-36 completely.

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x'+4x²-9x-36>0 x²(x+4)-9(x+4)>0 (x+4)(x²-9)>0 (x+4)(x²-3²)>0 (x+4)(x+3)(x-3)>0

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Step 2

Setting (x+4)(x+3)(x-3)=0 we get x=-4, -3, 3

 

Step 3

Check sign of (x+4)(x+3)(x-3) in each interval.

Pick a real number in each...

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-4 -3.5 - 3

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