Identify the Zeros and Their Multiplicities f(x)=3(x+3)(x+6)^3

$f (x) = 3 (x + 3) {(x + 6)}^{3}$

Step 1

Set $3 (x + 3) {(x + 6)}^{3}$ equal to $0$ .

$3 (x + 3) {(x + 6)}^{3} = 0$

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 $0$ .

$x + 3 = 0$

${(x + 6)}^{3} = 0$

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 ${(x + 6)}^{3}$ equal to $0$ and solve for $x$ .

Set ${(x + 6)}^{3}$ equal to $0$ .

${(x + 6)}^{3} = 0$

Solve ${(x + 6)}^{3} = 0$ for $x$ .

Set the $x + 6$ equal to $0$ .

$x + 6 = 0$

Subtract $6$ from both sides of the equation.

$x = - 6$

The final solution is all the values that make $3 (x + 3) {(x + 6)}^{3} = 0$ true. The multiplicity of a root is the number of times the root appears.

$x = - 3$ (Multiplicity of $1$ )

$x = - 6$ (Multiplicity of $3$ )

$x = - 3$ (Multiplicity of $1$ )

$x = - 6$ (Multiplicity of $3$ )

Step 3

Identify the Zeros and Their Multiplicities f(x)=3(x+3)(x+6)^3

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