Solve (x^2)(3 - x)(x 1) > 0

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve the inequality by separating into cases

0 < x < 3

Alternative Form

x \in (0, 3)

Evaluate

x^{2} (3 - x) (x \times 1) > 0

Remove the parentheses

x^{2} (3 - x) x \times 1 > 0

Multiply the terms

More Steps

x^{3} (3 - x) > 0

Rewrite the expression

x^{3} (3 - x) = 0

Separate the equation into 2 possible cases

x^{3} = 0 3 - x = 0

The only way a power can be 0 is when the base equals 0

x = 0 3 - x = 0

Solve the equation

More Steps

x = 0 x = 3

Determine the test intervals using the critical values

x < 0 0 < x < 3 x > 3

Choose a value form each interval

x_{1} = - 1 x_{2} = 2 x_{3} = 4

To determine if x < 0 is the solution to the inequality,test if the chosen value x = - 1 satisfies the initial inequality

More Steps

x < 0 is not a solution x_{2} = 2 x_{3} = 4

To determine if 0 < x < 3 is the solution to the inequality,test if the chosen value x = 2 satisfies the initial inequality

More Steps

x < 0 is not a solution 0 < x < 3 is the solution x_{3} = 4

To determine if x > 3 is the solution to the inequality,test if the chosen value x = 4 satisfies the initial inequality

More Steps

x < 0 is not a solution 0 < x < 3 is the solution x > 3 is not a solution

Solution

0 < x < 3

Alternative Form

x \in (0, 3)

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