Solve x^3-13x^2-30x

Question

Factor the expression

x (x - 15) (x + 2)

Evaluate

x^{3} - 13 x^{2} - 30 x

Rewrite the expression

x \times x^{2} - x \times 13 x - x \times 30

Factor out x from the expression

x (x^{2} - 13 x - 30)

Solution

More Steps

Evaluate

x^{2} - 13 x - 30

Rewrite the expression

x^{2} + (2 - 15) x - 30

Calculate

x^{2} + 2 x - 15 x - 30

Rewrite the expression

x \times x + x \times 2 - 15 x - 15 \times 2

Factor out x from the expression

x (x + 2) - 15 x - 15 \times 2

Factor out - 15 from the expression

x (x + 2) - 15 (x + 2)

Factor out x + 2 from the expression

(x - 15) (x + 2)

x (x - 15) (x + 2)

Show Solution

x_{1} = - 2, x_{2} = 0, x_{3} = 15

Evaluate

x^{3} - 13 x^{2} - 30 x

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

x^{3} - 13 x^{2} - 30 x = 0

Factor the expression

x (x - 15) (x + 2) = 0

Separate the equation into 3 possible cases

x = 0 x - 15 = 0 x + 2 = 0

Solve the equation

More Steps

Evaluate

x - 15 = 0

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

x = 0 + 15

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

x = 15

x = 0 x = 15 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 = 0 x = 15 x = - 2

Solution

x_{1} = - 2, x_{2} = 0, x_{3} = 15

Show Solution