Identify the Zeros and Their Multiplicities x^2(x+2)(x-2)

$x^{2} (x + 2) (x - 2)$

Step 1

Set $x^{2} (x + 2) (x - 2)$ equal to $0$ .

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

Step 2

Solve for $x$ .

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

$x^{2} = 0$

$x + 2 = 0$

$x - 2 = 0$

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

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

$x^{2} = 0$

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

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

$x = \pm \sqrt{0}$

Simplify $\pm \sqrt{0}$ .

Rewrite $0$ as $0^{2}$ .

$x = \pm \sqrt{0^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm 0$

Plus or minus $0$ is $0$ .

$x = 0$

Set $x + 2$ equal to $0$ and solve for $x$ .

Set $x + 2$ equal to $0$ .

$x + 2 = 0$

Subtract $2$ from both sides of the equation.

$x = - 2$

Set $x - 2$ equal to $0$ and solve for $x$ .

Set $x - 2$ equal to $0$ .

$x - 2 = 0$

Add $2$ to both sides of the equation.

$x = 2$

The final solution is all the values that make $x^{2} (x + 2) (x - 2) = 0$ true. The multiplicity of a root is the number of times the root appears.

$x = 0$ (Multiplicity of $2$ )

$x = - 2$ (Multiplicity of $1$ )

$x = 2$ (Multiplicity of $1$ )

$x = 0$ (Multiplicity of $2$ )

$x = - 2$ (Multiplicity of $1$ )

$x = 2$ (Multiplicity of $1$ )

Step 3