Find the Roots (Zeros) f(x)=(x+5)^3(x-9)(x+1)

$f (x) = {(x + 5)}^{3} (x - 9) (x + 1)$

Step 1

Set ${(x + 5)}^{3} (x - 9) (x + 1)$ equal to $0$ .

${(x + 5)}^{3} (x - 9) (x + 1) = 0$

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 $0$ .

${(x + 5)}^{3} = 0$

$x - 9 = 0$

$x + 1 = 0$

Set ${(x + 5)}^{3}$ equal to $0$ and solve for $x$ .

Set ${(x + 5)}^{3}$ equal to $0$ .

${(x + 5)}^{3} = 0$

Solve ${(x + 5)}^{3} = 0$ for $x$ .

Set the $x + 5$ equal to $0$ .

$x + 5 = 0$

Subtract $5$ from both sides of the equation.

$x = - 5$

Set $x - 9$ equal to $0$ and solve for $x$ .

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

$x - 9 = 0$

Add $9$ to both sides of the equation.

$x = 9$

Set $x + 1$ equal to $0$ and solve for $x$ .

Set $x + 1$ equal to $0$ .

$x + 1 = 0$

Subtract $1$ from both sides of the equation.

$x = - 1$

The final solution is all the values that make ${(x + 5)}^{3} (x - 9) (x + 1) = 0$ true.

$x = - 5, 9, - 1$

Step 3