Identify the Zeros and Their Multiplicities (x-7)(x-5)(x-5)(x+2)

$(x - 7) (x - 5) (x - 5) (x + 2)$

Step 1

Set $(x - 7) (x - 5) (x - 5) (x + 2)$ equal to $0$ .

$(x - 7) (x - 5) (x - 5) (x + 2) = 0$

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 $0$ .

$x - 7 = 0$

$x - 5 = 0$

$x + 2 = 0$

Set $x - 7$ equal to $0$ and solve for $x$ .

Set $x - 7$ equal to $0$ .

$x - 7 = 0$

Add $7$ to both sides of the equation.

$x = 7$

Set $x - 5$ equal to $0$ and solve for $x$ .

Set $x - 5$ equal to $0$ .

$x - 5 = 0$

Add $5$ to both sides of the equation.

$x = 5$

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.

$x = - 2$

The final solution is all the values that make $(x - 7) (x - 5) (x - 5) (x + 2) = 0$ true. The multiplicity of a root is the number of times the root appears.

$x = 7$ (Multiplicity of $1$ )

$x = 5$ (Multiplicity of $2$ )

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

$x = 7$ (Multiplicity of $1$ )

$x = 5$ (Multiplicity of $2$ )

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

Step 3

Identify the Zeros and Their Multiplicities (x-7)(x-5)(x-5)(x+2)

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