Identify the Zeros and Their Multiplicities f(x)=3(x-5)(x-4)(x+2)(x+9)

$f (x) = 3 (x - 5) (x - 4) (x + 2) (x + 9)$

Step 1

Set $3 (x - 5) (x - 4) (x + 2) (x + 9)$ equal to $0$ .

$3 (x - 5) (x - 4) (x + 2) (x + 9) = 0$

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 $0$ .

$x - 5 = 0$

$x - 4 = 0$

$x + 2 = 0$

$x + 9 = 0$

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 $x - 4$ equal to $0$ and solve for $x$ .

Set $x - 4$ equal to $0$ .

$x - 4 = 0$

Add $4$ to both sides of the equation.

$x = 4$

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 $x + 9$ equal to $0$ and solve for $x$ .

Set $x + 9$ equal to $0$ .

$x + 9 = 0$

Subtract $9$ from both sides of the equation.

$x = - 9$

The final solution is all the values that make $3 (x - 5) (x - 4) (x + 2) (x + 9) = 0$ true. The multiplicity of a root is the number of times the root appears.

$x = 5$ (Multiplicity of $1$ )

$x = 4$ (Multiplicity of $1$ )

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

$x = - 9$ (Multiplicity of $1$ )

$x = 5$ (Multiplicity of $1$ )

$x = 4$ (Multiplicity of $1$ )

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

$x = - 9$ (Multiplicity of $1$ )

Step 3

Identify the Zeros and Their Multiplicities f(x)=3(x-5)(x-4)(x+2)(x+9)

Related Questions

Support LCMGCF.com by disabling your adblocker.