Solve 5x^3 -35x^2 +50x

Question

Factor the expression

5 x (x - 5) (x - 2)

Evaluate

5 x^{3} - 35 x^{2} + 50 x

Rewrite the expression

5 x \times x^{2} - 5 x \times 7 x + 5 x \times 10

Factor out 5 x from the expression

5 x (x^{2} - 7 x + 10)

Solution

More Steps

Evaluate

x^{2} - 7 x + 10

Rewrite the expression

x^{2} + (- 2 - 5) x + 10

Calculate

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

Rewrite the expression

x \times x - x \times 2 - 5 x + 5 \times 2

Factor out x from the expression

x (x - 2) - 5 x + 5 \times 2

Factor out - 5 from the expression

x (x - 2) - 5 (x - 2)

Factor out x - 2 from the expression

(x - 5) (x - 2)

5 x (x - 5) (x - 2)

Show Solution

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

Evaluate

5 x^{3} - 35 x^{2} + 50 x

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

5 x^{3} - 35 x^{2} + 50 x = 0

Factor the expression

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

Divide both sides

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

Separate the equation into 3 possible cases

x = 0 x - 5 = 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 = 0 x = 5 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 = 5 x = 2

Solution

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

Show Solution