Solve 8x^3-16x^2-120x

Question

Factor the expression

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

Evaluate

8 x^{3} - 16 x^{2} - 120 x

Rewrite the expression

8 x \times x^{2} - 8 x \times 2 x - 8 x \times 15

Factor out 8 x from the expression

8 x (x^{2} - 2 x - 15)

Solution

More Steps

Evaluate

x^{2} - 2 x - 15

Rewrite the expression

x^{2} + (3 - 5) x - 15

Calculate

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

Rewrite the expression

x \times x + x \times 3 - 5 x - 5 \times 3

Factor out x from the expression

x (x + 3) - 5 x - 5 \times 3

Factor out - 5 from the expression

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

Factor out x + 3 from the expression

(x - 5) (x + 3)

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

Show Solution

x_{1} = - 3, x_{2} = 0, x_{3} = 5

Evaluate

8 x^{3} - 16 x^{2} - 120 x

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

8 x^{3} - 16 x^{2} - 120 x = 0

Factor the expression

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

Divide both sides

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

Separate the equation into 3 possible cases

x = 0 x - 5 = 0 x + 3 = 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 = 0 x = 5 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 = 5 x = - 3

Solution

x_{1} = - 3, x_{2} = 0, x_{3} = 5

Show Solution