Solve x^3-2x^2-13x-10

Question

Factor the expression

(x - 5) (x + 1) (x + 2)

Evaluate

x^{3} - 2 x^{2} - 13 x - 10

Calculate

x^{3} + 3 x^{2} + 2 x - 5 x^{2} - 15 x - 10

Rewrite the expression

x \times x^{2} + x \times 3 x + x \times 2 - 5 x^{2} - 5 \times 3 x - 5 \times 2

Factor out x from the expression

x (x^{2} + 3 x + 2) - 5 x^{2} - 5 \times 3 x - 5 \times 2

Factor out - 5 from the expression

x (x^{2} + 3 x + 2) - 5 (x^{2} + 3 x + 2)

Factor out x^{2} + 3 x + 2 from the expression

(x - 5) (x^{2} + 3 x + 2)

Solution

More Steps

Evaluate

x^{2} + 3 x + 2

Rewrite the expression

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

Calculate

x^{2} + 2 x + x + 2

Rewrite the expression

x \times x + x \times 2 + x + 2

Factor out x from the expression

x (x + 2) + x + 2

Factor out x + 2 from the expression

(x + 1) (x + 2)

(x - 5) (x + 1) (x + 2)

Show Solution

x_{1} = - 2, x_{2} = - 1, x_{3} = 5

Evaluate

x^{3} - 2 x^{2} - 13 x - 10

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

x^{3} - 2 x^{2} - 13 x - 10 = 0

Factor the expression

(x - 5) (x + 1) (x + 2) = 0

Separate the equation into 3 possible cases

x - 5 = 0 x + 1 = 0 x + 2 = 0

Solve the equation

More Steps

Evaluate

x - 5 = 0

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

x = 0 + 5

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

x = 5

x = 5 x + 1 = 0 x + 2 = 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 = 5 x = - 1 x + 2 = 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 = 5 x = - 1 x = - 2

Solution

x_{1} = - 2, x_{2} = - 1, x_{3} = 5

Show Solution