Solve 3x^3 - x - ScanMath

Question

Factor the expression

x (3 x^{2} - 1)

Evaluate

3 x^{3} - x

Rewrite the expression

x \times 3 x^{2} - x

Solution

x (3 x^{2} - 1)

Show Solution

x_{1} = - \frac{3}{3}, x_{2} = 0, x_{3} = \frac{3}{3}

Alternative Form

x_{1} \approx - 0.57735, x_{2} = 0, x_{3} \approx 0.57735

Evaluate

3 x^{3} - x

To find the roots of the expression,set the expression equal to 0

3 x^{3} - x = 0

Factor the expression

x (3 x^{2} - 1) = 0

Separate the equation into 2 possible cases

x = 0 3 x^{2} - 1 = 0

Solve the equation

More Steps

Evaluate

3 x^{2} - 1 = 0

Move the constant to the right-hand side and change its sign

3 x^{2} = 0 + 1

Removing 0 doesn't change the value,so remove it from the expression

3 x^{2} = 1

Divide both sides

\frac{3 x ^{2}}{3} = \frac{1}{3}

Divide the numbers

x^{2} = \frac{1}{3}

Take the root of both sides of the equation and remember to use both positive and negative roots

x = \pm \frac{1}{3}

Simplify the expression

More Steps

Evaluate

\frac{1}{3}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{1}{3}

Simplify the radical expression

\frac{1}{3}

Multiply by the Conjugate

\frac{3}{3 \times 3}

When a square root of an expression is multiplied by itself,the result is that expression

\frac{3}{3}

x = \pm \frac{3}{3}

Separate the equation into 2 possible cases

x = \frac{3}{3} x = - \frac{3}{3}

x = 0 x = \frac{3}{3} x = - \frac{3}{3}

Solution

x_{1} = - \frac{3}{3}, x_{2} = 0, x_{3} = \frac{3}{3}

Alternative Form

x_{1} \approx - 0.57735, x_{2} = 0, x_{3} \approx 0.57735

Show Solution