Solve the inequality.

x^3 + x^2 < 12x

Write your answer as an interval or a union of intervals.

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factor x

x(x^2+x)< 12x divide by in both sides

x^2+x< 12

x^2+x-12< 0

sum=1 product=-12 factors are=4,-3

x^2+4x-3x+12<0

x(x+4)-3(x+4)<0

(x-3)(x+4)<0

therefore the values of x lies between -4 and 3 which can be written as

-4<x<3

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