Find the x and y Intercepts f(x)=x(x+2)(x-3)(x+4)

$f (x) = x (x + 2) (x - 3) (x + 4)$

Step 1

Find the x-intercepts.

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

$0 = x (x + 2) (x - 3) (x + 4)$

Solve the equation.

Rewrite the equation as $x (x + 2) (x - 3) (x + 4) = 0$ .

$x (x + 2) (x - 3) (x + 4) = 0$

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

$x = 0$

$x + 2 = 0$

$x - 3 = 0$

$x + 4 = 0$

Set $x$ equal to $0$ .

$x = 0$

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 $x - 3$ equal to $0$ and solve for $x$ .

Set $x - 3$ equal to $0$ .

$x - 3 = 0$

Add $3$ to both sides of the equation.

$x = 3$

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 $x (x + 2) (x - 3) (x + 4) = 0$ true.

$x = 0, - 2, 3, - 4$

x-intercept(s) in point form.

x-intercept(s): $(0, 0), (- 2, 0), (3, 0), (- 4, 0)$

Step 2

Find the y-intercepts.

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

$y = (0) ((0) + 2) ((0) - 3) ((0) + 4)$

Solve the equation.

Remove parentheses.

$y = 0 (0 + 2) ((0) - 3) ((0) + 4)$

Remove parentheses.

$y = 0 (0 + 2) (0 - 3) ((0) + 4)$

Remove parentheses.

$y = 0 (0 + 2) (0 - 3) (0 + 4)$

Remove parentheses.

$y = (0) ((0) + 2) ((0) - 3) ((0) + 4)$

Simplify $(0) ((0) + 2) ((0) - 3) ((0) + 4)$ .

Add $0$ and $2$ .

$y = 0 \cdot 2 ((0) - 3) ((0) + 4)$

Multiply $0$ by $2$ .

$y = 0 ((0) - 3) ((0) + 4)$

Subtract $3$ from $0$ .

$y = 0 \cdot - 3 ((0) + 4)$

Multiply $0$ by $- 3$ .

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

Add $0$ and $4$ .

$y = 0 \cdot 4$

Multiply $0$ by $4$ .

$y = 0$

y-intercept(s) in point form.

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

Step 3

List the intersections.

x-intercept(s): $(0, 0), (- 2, 0), (3, 0), (- 4, 0)$

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

Step 4

Find the x and y Intercepts f(x)=x(x+2)(x-3)(x+4)

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