Identify the Zeros and Their Multiplicities x^5-2x^4

$x^{5} - 2 x^{4}$

Step 1

Set $x^{5} - 2 x^{4}$ equal to $0$ .

$x^{5} - 2 x^{4} = 0$

Step 2

Solve for $x$ .

Factor $x^{4}$ out of $x^{5} - 2 x^{4}$ .

Factor $x^{4}$ out of $x^{5}$ .

$x^{4} x - 2 x^{4} = 0$

Factor $x^{4}$ out of $- 2 x^{4}$ .

$x^{4} x + x^{4} \cdot - 2 = 0$

Factor $x^{4}$ out of $x^{4} x + x^{4} \cdot - 2$ .

$x^{4} (x - 2) = 0$

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

$x^{4} = 0$

$x - 2 = 0$

Set $x^{4}$ equal to $0$ and solve for $x$ .

Set $x^{4}$ equal to $0$ .

$x^{4} = 0$

Solve $x^{4} = 0$ for $x$ .

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

$x = \pm \sqrt[4]{0}$

Simplify $\pm \sqrt[4]{0}$ .

Rewrite $0$ as $0^{4}$ .

$x = \pm \sqrt[4]{0^{4}}$

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 $0$ .

$x - 2 = 0$

Add $2$ to both sides of the equation.

$x = 2$

The final solution is all the values that make $x^{4} (x - 2) = 0$ true. The multiplicity of a root is the number of times the root appears.

$x = 0$ (Multiplicity of $4$ )

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

$x = 0$ (Multiplicity of $4$ )

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

Step 3