Solve 2x^3-x^2-x - ScanMath

Question

Factor the expression

x (x - 1) (2 x + 1)

Evaluate

2 x^{3} - x^{2} - x

Rewrite the expression

x \times 2 x^{2} - x \times x - x

Factor out x from the expression

x (2 x^{2} - x - 1)

Solution

More Steps

Evaluate

2 x^{2} - x - 1

Rewrite the expression

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

Calculate

2 x^{2} + x - 2 x - 1

Rewrite the expression

x \times 2 x + x - 2 x - 1

Factor out x from the expression

x (2 x + 1) - 2 x - 1

Factor out - 1 from the expression

x (2 x + 1) - (2 x + 1)

Factor out 2 x + 1 from the expression

(x - 1) (2 x + 1)

x (x - 1) (2 x + 1)

Show Solution

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

Alternative Form

x_{1} = - 0.5, x_{2} = 0, x_{3} = 1

Evaluate

2 x^{3} - x^{2} - x

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

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

Factor the expression

x (x - 1) (2 x + 1) = 0

Separate the equation into 3 possible cases

x = 0 x - 1 = 0 2 x + 1 = 0

Solve the equation

More Steps

Evaluate

x - 1 = 0

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

x = 0 + 1

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

x = 1

x = 0 x = 1 2 x + 1 = 0

Solve the equation

More Steps

Evaluate

2 x + 1 = 0

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

2 x = 0 - 1

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

2 x = - 1

Divide both sides

\frac{2 x}{2} = \frac{- 1}{2}

Divide the numbers

x = \frac{- 1}{2}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

x = - \frac{1}{2}

x = 0 x = 1 x = - \frac{1}{2}

Solution

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

Alternative Form

x_{1} = - 0.5, x_{2} = 0, x_{3} = 1

Show Solution