Solve 5x^3-25x^2-120x

Question

Factor the expression

5 x (x - 8) (x + 3)

Evaluate

5 x^{3} - 25 x^{2} - 120 x

Rewrite the expression

5 x \times x^{2} - 5 x \times 5 x - 5 x \times 24

Factor out 5 x from the expression

5 x (x^{2} - 5 x - 24)

Solution

More Steps

Evaluate

x^{2} - 5 x - 24

Rewrite the expression

x^{2} + (3 - 8) x - 24

Calculate

x^{2} + 3 x - 8 x - 24

Rewrite the expression

x \times x + x \times 3 - 8 x - 8 \times 3

Factor out x from the expression

x (x + 3) - 8 x - 8 \times 3

Factor out - 8 from the expression

x (x + 3) - 8 (x + 3)

Factor out x + 3 from the expression

(x - 8) (x + 3)

5 x (x - 8) (x + 3)

Show Solution

x_{1} = - 3, x_{2} = 0, x_{3} = 8

Evaluate

5 x^{3} - 25 x^{2} - 120 x

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

5 x^{3} - 25 x^{2} - 120 x = 0

Factor the expression

5 x (x - 8) (x + 3) = 0

Divide both sides

x (x - 8) (x + 3) = 0

Separate the equation into 3 possible cases

x = 0 x - 8 = 0 x + 3 = 0

Solve the equation

More Steps

Evaluate

x - 8 = 0

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

x = 0 + 8

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

x = 8

x = 0 x = 8 x + 3 = 0

Solve the equation

More Steps

Evaluate

x + 3 = 0

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

x = 0 - 3

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

x = - 3

x = 0 x = 8 x = - 3

Solution

x_{1} = - 3, x_{2} = 0, x_{3} = 8

Show Solution