Identify the Zeros and Their Multiplicities y=(x-2)(x+7)^3

$y = (x - 2) {(x + 7)}^{3}$

Step 1

Set $(x - 2) {(x + 7)}^{3}$ equal to $0$ .

$(x - 2) {(x + 7)}^{3} = 0$

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 $0$ .

$x - 2 = 0$

${(x + 7)}^{3} = 0$

Set $x - 2$ equal to $0$ and solve for $x$ .

Set $x - 2$ equal to $0$ .

$x - 2 = 0$

Add $2$ to both sides of the equation.

$x = 2$

Set ${(x + 7)}^{3}$ equal to $0$ and solve for $x$ .

Set ${(x + 7)}^{3}$ equal to $0$ .

${(x + 7)}^{3} = 0$

Solve ${(x + 7)}^{3} = 0$ for $x$ .

Set the $x + 7$ equal to $0$ .

$x + 7 = 0$

Subtract $7$ from both sides of the equation.

$x = - 7$

The final solution is all the values that make $(x - 2) {(x + 7)}^{3} = 0$ true. The multiplicity of a root is the number of times the root appears.

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

$x = - 7$ (Multiplicity of $3$ )

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

$x = - 7$ (Multiplicity of $3$ )

Step 3