Find the x and y Intercepts x(x+1)(x-5)(x-7)

$x (x + 1) (x - 5) (x - 7)$

Step 1

Write $x (x + 1) (x - 5) (x - 7)$ as an equation.

$y = x (x + 1) (x - 5) (x - 7)$

Step 2

Find the x-intercepts.

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

$0 = x (x + 1) (x - 5) (x - 7)$

Solve the equation.

Rewrite the equation as $x (x + 1) (x - 5) (x - 7) = 0$ .

$x (x + 1) (x - 5) (x - 7) = 0$

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

$x = 0$

$x + 1 = 0$

$x - 5 = 0$

$x - 7 = 0$

Set $x$ equal to $0$ .

$x = 0$

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.

$x = - 1$

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

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

$x - 5 = 0$

Add $5$ to both sides of the equation.

$x = 5$

Set $x - 7$ equal to $0$ and solve for $x$ .

Set $x - 7$ equal to $0$ .

$x - 7 = 0$

Add $7$ to both sides of the equation.

$x = 7$

The final solution is all the values that make $x (x + 1) (x - 5) (x - 7) = 0$ true.

$x = 0, - 1, 5, 7$

x-intercept(s) in point form.

x-intercept(s): $(0, 0), (- 1, 0), (5, 0), (7, 0)$

Step 3

Find the y-intercepts.

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

$y = (0) ((0) + 1) ((0) - 5) ((0) - 7)$

Solve the equation.

Remove parentheses.

$y = 0 (0 + 1) ((0) - 5) ((0) - 7)$

Remove parentheses.

$y = 0 (0 + 1) (0 - 5) ((0) - 7)$

Remove parentheses.

$y = 0 (0 + 1) (0 - 5) (0 - 7)$

Remove parentheses.

$y = (0) ((0) + 1) ((0) - 5) ((0) - 7)$

Simplify $(0) ((0) + 1) ((0) - 5) ((0) - 7)$ .

Add $0$ and $1$ .

$y = 0 \cdot 1 ((0) - 5) ((0) - 7)$

Multiply $0$ by $1$ .

$y = 0 ((0) - 5) ((0) - 7)$

Subtract $5$ from $0$ .

$y = 0 \cdot - 5 ((0) - 7)$

Multiply $0$ by $- 5$ .

$y = 0 ((0) - 7)$

Subtract $7$ from $0$ .

$y = 0 \cdot - 7$

Multiply $0$ by $- 7$ .

$y = 0$

y-intercept(s) in point form.

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

Step 4

List the intersections.

x-intercept(s): $(0, 0), (- 1, 0), (5, 0), (7, 0)$

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

Step 5

Find the x and y Intercepts x(x+1)(x-5)(x-7)

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