Identify the Zeros and Their Multiplicities y=x(x-8)^2

$y = x {(x - 8)}^{2}$

Step 1

Set $x {(x - 8)}^{2}$ equal to $0$ .

$x {(x - 8)}^{2} = 0$

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 $0$ .

$x = 0$

${(x - 8)}^{2} = 0$

Set $x$ equal to $0$ .

$x = 0$

Set ${(x - 8)}^{2}$ equal to $0$ and solve for $x$ .

Set ${(x - 8)}^{2}$ equal to $0$ .

${(x - 8)}^{2} = 0$

Solve ${(x - 8)}^{2} = 0$ for $x$ .

Set the $x - 8$ equal to $0$ .

$x - 8 = 0$

Add $8$ to both sides of the equation.

$x = 8$

The final solution is all the values that make $x {(x - 8)}^{2} = 0$ true. The multiplicity of a root is the number of times the root appears.

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

$x = 8$ (Multiplicity of $2$ )

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

$x = 8$ (Multiplicity of $2$ )

Step 3