Solve x^3-5x^2+3x-15

Question

Factor the expression

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

Evaluate

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

Calculate

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

Rewrite the expression

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

Factor out x from the expression

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

Factor out - 5 from the expression

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

Solution

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

Show Solution

x_{1} = - 3 \times i, x_{2} = 3 \times i, x_{3} = 5

Alternative Form

x_{1} \approx - 1.732051 i, x_{2} \approx 1.732051 i, x_{3} = 5

Evaluate

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

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

x^{3} - 5 x^{2} + 3 x - 15 = 0

Factor the expression

(x - 5) (x^{2} + 3) = 0

Separate the equation into 2 possible cases

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

Solve the equation

More Steps

Evaluate

x^{2} + 3 = 0

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

x^{2} = 0 - 3

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

x^{2} = - 3

Take the root of both sides of the equation and remember to use both positive and negative roots

x = \pm - 3

Simplify the expression

More Steps

Evaluate

- 3

Evaluate the power

3 \times - 1

Evaluate the power

3 \times i

x = \pm (3 \times i)

Separate the equation into 2 possible cases

x = 3 \times i x = - 3 \times i

x = 5 x = 3 \times i x = - 3 \times i

Solution

x_{1} = - 3 \times i, x_{2} = 3 \times i, x_{3} = 5

Alternative Form

x_{1} \approx - 1.732051 i, x_{2} \approx 1.732051 i, x_{3} = 5

Show Solution