What is -3(x-2)(x+3)^2(x-11)>0 ?

The solution to -3(x-2)(x+3)^2(x-11)>0 is 2<x<11

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-3(x-2)(x+3)^2(x-11)>0

- 3 (x - 2) (x + 3)^{2} (x - 11) > 0

2 < x < 11

Solution steps

- 3 (x - 2) (x + 3)^{2} (x - 11) > 0

Rewrite in standard form

- x^{4} + 7 x^{3} + 47 x^{2} - 15 x - 198 > 0

Factor

- x^{4} + 7 x^{3} + 47 x^{2} - 15 x - 198 : - (x - 2) (x + 3)^{2} (x - 11)

- (x - 2) (x + 3)^{2} (x - 11) > 0

Multiply both sides by

- 1

(reverse the inequality)

(- (x - 2) (x + 3)^{2} (x - 11)) (- 1) < 0 \cdot (- 1)

Simplify

(x - 2) (x + 3)^{2} (x - 11) < 0

Identify the intervals

2 < x < 11

9 ∣ 3 n - 2 ∣ + 6 > 51

\frac{x + 5}{3} - \frac{1}{2} x + 3 (2 x - \frac{1}{2}) = 5 (\frac{x}{2} - 2)

24 \cdot 7

(\frac{y}{6})^{2}

\frac{144 + 9 ( 0 + 3 ) ^{2}}{16}

What is -3(x-2)(x+3)^2(x-11)>0 ?
The solution to -3(x-2)(x+3)^2(x-11)>0 is 2<x<11