Find the Roots (Zeros) x^3+3x^2-5x-15

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

Step 1

Set $x^{3} + 3 x^{2} - 5 x - 15$ equal to $0$ .

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

Step 2

Solve for $x$ .

Factor the left side of the equation.

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

Factor out the greatest common factor (GCF) from each group.

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

Factor the polynomial by factoring out the greatest common factor, $x + 3$ .

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

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x + 3 = 0$

$x^{2} - 5 = 0$

Set $x + 3$ equal to $0$ and solve for $x$ .

Set $x + 3$ equal to $0$ .

$x + 3 = 0$

Subtract $3$ from both sides of the equation.

$x = - 3$

Set $x^{2} - 5$ equal to $0$ and solve for $x$ .

Set $x^{2} - 5$ equal to $0$ .

$x^{2} - 5 = 0$

Solve $x^{2} - 5 = 0$ for $x$ .

Add $5$ to both sides of the equation.

$x^{2} = 5$

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{5}$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$x = \sqrt{5}$

Next, use the negative value of the $\pm$ to find the second solution.

$x = - \sqrt{5}$

The complete solution is the result of both the positive and negative portions of the solution.

$x = \sqrt{5}, - \sqrt{5}$

The final solution is all the values that make $(x + 3) (x^{2} - 5) = 0$ true.

$x = - 3, \sqrt{5}, - \sqrt{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = - 3, \sqrt{5}, - \sqrt{5}$

Decimal Form:

$x = - 3, 2.23606797 \dots, - 2.23606797 \dots$

Step 4

Find the Roots (Zeros) x^3+3x^2-5x-15

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