Solve x^3-2x^2-x+2

Question

Factor the expression

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

Evaluate

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

Calculate

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

Rewrite the expression

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

Factor out x from the expression

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

Factor out - 2 from the expression

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

Factor out x^{2} - 1 from the expression

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

Solution

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

Show Solution

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

Evaluate

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

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

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

Factor the expression

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

Separate the equation into 3 possible cases

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

Solve the equation

More Steps

Evaluate

x - 2 = 0

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

x = 0 + 2

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

x = 2

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

Solution

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

Show Solution