What is -x^3+8x^2+4x>32 ?

The solution to -x^3+8x^2+4x>32 is x<-2\lor 2<x<8

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-x^3+8x^2+4x>32

- x^{3} + 8 x^{2} + 4 x > 32

x < - 2 or 2 < x < 8

Solution steps

- x^{3} + 8 x^{2} + 4 x > 32

Rewrite in standard form

- x^{3} + 8 x^{2} + 4 x - 32 > 0

Factor

- x^{3} + 8 x^{2} + 4 x - 32 : - (x - 8) (x + 2) (x - 2)

- (x - 8) (x + 2) (x - 2) > 0

Multiply both sides by

- 1

(reverse the inequality)

(- (x - 8) (x + 2) (x - 2)) (- 1) < 0 \cdot (- 1)

Simplify

(x - 8) (x + 2) (x - 2) < 0

Identify the intervals

x < - 2 or 2 < x < 8

(7^{2})^{2}

1 - 5

\frac{6}{5} - 1