What is (x^3-1)(x^3+1)(3-x)*x>= 0 ?

The solution to (x^3-1)(x^3+1)(3-x)*x>= 0 is -1<= x<= 0\lor 1<= x<= 3

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(x^3-1)(x^3+1)(3-x)*x>= 0

(x^{3} - 1) (x^{3} + 1) (3 - x) \cdot x \geq 0

- 1 \leq x \leq 0 or 1 \leq x \leq 3

Interval Notation

[- 1, 0] \cup [1, 3]

Solution steps

(x^{3} - 1) (x^{3} + 1) (3 - x) x \geq 0

Factor

(x^{3} - 1) (x^{3} + 1) (3 - x) x : - x (x - 1) (x + 1) (x - 3) (x^{2} + x + 1) (x^{2} - x + 1)

- x (x - 1) (x + 1) (x - 3) (x^{2} + x + 1) (x^{2} - x + 1) \geq 0

Multiply both sides by

- 1

(reverse the inequality)

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

Simplify

x (x - 1) (x + 1) (x - 3) (x^{2} + x + 1) (x^{2} - x + 1) \leq 0

Identify the intervals

- 1 \leq x \leq 0 or 1 \leq x \leq 3

x < \frac{1}{x}

\frac{( 3 x - x ^{2} )}{( ( x + 4 ) ^{2} )} \geq 0

\frac{x}{x - 1} > \frac{1}{x}

\frac{( x + 5 )}{( x + 1 )} > 0

\frac{1}{( 2 x - 7 )} \geq 0

What is (x^3-1)(x^3+1)(3-x)*x>= 0 ?
The solution to (x^3-1)(x^3+1)(3-x)*x>= 0 is -1<= x<= 0\lor 1<= x<= 3