Algebra Examples

$f (x) = - 4 (x + 1) (x + 1) (x + 1) (x - 5)$

Step 1

Set $- 4 (x + 1) (x + 1) (x + 1) (x - 5)$ equal to $0$ .

$- 4 (x + 1) (x + 1) (x + 1) (x - 5) = 0$

Step 2

Solve for $x$ .

Tap for more steps...

Step 2.1

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x + 1 = 0$

$x - 5 = 0$

Step 2.2

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

Tap for more steps...

Step 2.2.1

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

$x + 1 = 0$

Step 2.2.2

Subtract $1$ from both sides of the equation.

$x = - 1$

Step 2.3

Set $x - 5$ equal to $0$ and solve for $x$ .

Tap for more steps...

Step 2.3.1

Set $x - 5$ equal to $0$ .

$x - 5 = 0$

Step 2.3.2

Add $5$ to both sides of the equation.

$x = 5$

Step 2.4

The final solution is all the values that make $- 4 (x + 1) (x + 1) (x + 1) (x - 5) = 0$ true. The multiplicity of a root is the number of times the root appears.

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

$x = 5$ (Multiplicity of $1$ )

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

$x = 5$ (Multiplicity of $1$ )

Step 3