What is -x^3+8x^2+9x>72 ?

The solution to -x^3+8x^2+9x>72 is x<-3\lor 3<x<8

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-x^3+8x^2+9x>72

- x^{3} + 8 x^{2} + 9 x > 72

x < - 3 or 3 < x < 8

Interval Notation

(- \infty, - 3) \cup (3, 8)

Solution steps

- x^{3} + 8 x^{2} + 9 x > 72

Rewrite in standard form

- x^{3} + 8 x^{2} + 9 x - 72 > 0

Factor

- x^{3} + 8 x^{2} + 9 x - 72 : - (x - 8) (x + 3) (x - 3)

- (x - 8) (x + 3) (x - 3) > 0

Multiply both sides by

- 1

(reverse the inequality)

(- (x - 8) (x + 3) (x - 3)) (- 1) < 0 \cdot (- 1)

Simplify

(x - 8) (x + 3) (x - 3) < 0

Identify the intervals

x < - 3 or 3 < x < 8

4 > h

- 4 (w + 4) = 3 (w + 4) + 7

4 x y^{2} + 24 x^{2} y^{6}

\frac{5 ^{9}}{5 ^{3}}

d^{2} + 10 d + 21