Precalculus Examples

$f (x) = - 4 (x + 4) {(x - 4)}^{3}$

Step 1

Set $- 4 (x + 4) {(x - 4)}^{3}$ equal to $0$ .

$- 4 (x + 4) {(x - 4)}^{3} = 0$

Step 2

Solve for $x$ .

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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 $0$ .

$x + 4 = 0$

${(x - 4)}^{3} = 0$

Step 2.2

Set $x + 4$ equal to $0$ and solve for $x$ .

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Step 2.2.1

Set $x + 4$ equal to $0$ .

$x + 4 = 0$

Step 2.2.2

Subtract $4$ from both sides of the equation.

$x = - 4$

Step 2.3

Set ${(x - 4)}^{3}$ equal to $0$ and solve for $x$ .

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Step 2.3.1

Set ${(x - 4)}^{3}$ equal to $0$ .

${(x - 4)}^{3} = 0$

Step 2.3.2

Solve ${(x - 4)}^{3} = 0$ for $x$ .

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Step 2.3.2.1

Set the $x - 4$ equal to $0$ .

$x - 4 = 0$

Step 2.3.2.2

Add $4$ to both sides of the equation.

$x = 4$

Step 2.4

The final solution is all the values that make $- 4 (x + 4) {(x - 4)}^{3} = 0$ true.

$x = - 4, 4$

Step 3