Identify the Zeros and Their Multiplicities y=3x(x+2)^3

$y = 3 x {(x + 2)}^{3}$

Step 1

Set $3 x {(x + 2)}^{3}$ equal to $0$ .

$3 x {(x + 2)}^{3} = 0$

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 $0$ .

$x = 0$

${(x + 2)}^{3} = 0$

Set $x$ equal to $0$ .

$x = 0$

Set ${(x + 2)}^{3}$ equal to $0$ and solve for $x$ .

Set ${(x + 2)}^{3}$ equal to $0$ .

${(x + 2)}^{3} = 0$

Solve ${(x + 2)}^{3} = 0$ for $x$ .

Set the $x + 2$ 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 $3 x {(x + 2)}^{3} = 0$ true. The multiplicity of a root is the number of times the root appears.

$x = 0$ (Multiplicity of $1$ )

$x = - 2$ (Multiplicity of $3$ )

$x = 0$ (Multiplicity of $1$ )

$x = - 2$ (Multiplicity of $3$ )

Step 3