Find the x and y Intercepts f(x)=(x^2-5)(x+6)

$f (x) = (x^{2} - 5) (x + 6)$

Step 1

Find the x-intercepts.

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

$0 = (x^{2} - 5) (x + 6)$

Solve the equation.

Rewrite the equation as $(x^{2} - 5) (x + 6) = 0$ .

$(x^{2} - 5) (x + 6) = 0$

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

$x^{2} - 5 = 0$

$x + 6 = 0$

Set $x^{2} - 5$ equal to $0$ and solve for $x$ .

Set $x^{2} - 5$ equal to $0$ .

$x^{2} - 5 = 0$

Solve $x^{2} - 5 = 0$ for $x$ .

Add $5$ to both sides of the equation.

$x^{2} = 5$

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{5}$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$x = \sqrt{5}$

Next, use the negative value of the $\pm$ to find the second solution.

$x = - \sqrt{5}$

The complete solution is the result of both the positive and negative portions of the solution.

$x = \sqrt{5}, - \sqrt{5}$

Set $x + 6$ equal to $0$ and solve for $x$ .

Set $x + 6$ equal to $0$ .

$x + 6 = 0$

Subtract $6$ from both sides of the equation.

$x = - 6$

The final solution is all the values that make $(x^{2} - 5) (x + 6) = 0$ true.

$x = \sqrt{5}, - \sqrt{5}, - 6$

x-intercept(s) in point form.

x-intercept(s): $(\sqrt{5}, 0), (- \sqrt{5}, 0), (- 6, 0)$

Step 2

Find the y-intercepts.

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

$y = ({(0)}^{2} - 5) ((0) + 6)$

Solve the equation.

Remove parentheses.

$y = (0^{2} - 5) ((0) + 6)$

Remove parentheses.

$y = (0^{2} - 5) (0 + 6)$

Remove parentheses.

$y = ({(0)}^{2} - 5) ((0) + 6)$

Simplify $({(0)}^{2} - 5) ((0) + 6)$ .

Raising $0$ to any positive power yields $0$ .

$y = (0 - 5) ((0) + 6)$

Subtract $5$ from $0$ .

$y = - 5 ((0) + 6)$

Add $0$ and $6$ .

$y = - 5 \cdot 6$

Multiply $- 5$ by $6$ .

$y = - 30$

y-intercept(s) in point form.

y-intercept(s): $(0, - 30)$

Step 3

List the intersections.

x-intercept(s): $(\sqrt{5}, 0), (- \sqrt{5}, 0), (- 6, 0)$

y-intercept(s): $(0, - 30)$

Step 4

Find the x and y Intercepts f(x)=(x^2-5)(x+6)

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