Find the x and y Intercepts f(x)=(2-x)(x+2)(x+4)

$f (x) = (2 - x) (x + 2) (x + 4)$

Find the x-intercepts.

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$0 = (2 - x) (x + 2) (x + 4)$

Solve the equation.

Rewrite the equation as $(2 - x) (x + 2) (x + 4) = 0$ .

$(2 - x) (x + 2) (x + 4) = 0$

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

$2 - x = 0$

$x + 2 = 0$

$x + 4 = 0$

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

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

$2 - x = 0$

Solve $2 - x = 0$ for $x$ .

Subtract $2$ from both sides of the equation.

$- x = - 2$

Divide each term in $- x = - 2$ by $- 1$ and simplify.

Divide each term in $- x = - 2$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 2}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 2}{- 1}$

Divide $x$ by $1$ .

$x = \frac{- 2}{- 1}$

Simplify the right side.

Divide $- 2$ by $- 1$ .

$x = 2$

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

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

$x + 2 = 0$

Subtract $2$ from both sides of the equation.

$x = - 2$

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

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

$x + 4 = 0$

Subtract $4$ from both sides of the equation.

$x = - 4$

The final solution is all the values that make $(2 - x) (x + 2) (x + 4) = 0$ true.

$x = 2, - 2, - 4$

x-intercept(s) in point form.

x-intercept(s): $(2, 0), (- 2, 0), (- 4, 0)$

Find the y-intercepts.

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$y = (2 - (0)) ((0) + 2) ((0) + 4)$

Solve the equation.

Remove parentheses.

$y = (2 - (0)) (0 + 2) ((0) + 4)$

Remove parentheses.

$y = (2 - (0)) (0 + 2) (0 + 4)$

Remove parentheses.

$y = (2 - (0)) ((0) + 2) ((0) + 4)$

Simplify $(2 - (0)) ((0) + 2) ((0) + 4)$ .

Subtract $0$ from $2$ .

$y = 2 ((0) + 2) ((0) + 4)$

Add $0$ and $2$ .

$y = 2 \cdot 2 ((0) + 4)$

Multiply $2$ by $2$ .

$y = 4 ((0) + 4)$

Add $0$ and $4$ .

$y = 4 \cdot 4$

Multiply $4$ by $4$ .

$y = 16$

y-intercept(s) in point form.

y-intercept(s): $(0, 16)$

List the intersections.

x-intercept(s): $(2, 0), (- 2, 0), (- 4, 0)$

y-intercept(s): $(0, 16)$

Find the x and y Intercepts f(x)=(2-x)(x+2)(x+4)

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