Find the x and y Intercepts p(x)=(x^2-9)(x^2+x-2)

$p (x) = (x^{2} - 9) (x^{2} + x - 2)$

Step 1

Find the x-intercepts.

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

$0 = (x^{2} - 9) (x^{2} + x - 2)$

Solve the equation.

Rewrite the equation as $(x^{2} - 9) (x^{2} + x - 2) = 0$ .

$(x^{2} - 9) (x^{2} + x - 2) = 0$

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

$x^{2} - 9 = 0$

$x^{2} + x - 2 = 0$

Set $x^{2} - 9$ equal to $0$ and solve for $x$ .

Set $x^{2} - 9$ equal to $0$ .

$x^{2} - 9 = 0$

Solve $x^{2} - 9 = 0$ for $x$ .

Add $9$ to both sides of the equation.

$x^{2} = 9$

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

$x = \pm \sqrt{9}$

Simplify $\pm \sqrt{9}$ .

Rewrite $9$ as $3^{2}$ .

$x = \pm \sqrt{3^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm 3$

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.

$x = 3$

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

$x = - 3$

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

$x = 3, - 3$

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

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

$x^{2} + x - 2 = 0$

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

Factor $x^{2} + x - 2$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 2$ and whose sum is $1$ .

$- 1, 2$

Write the factored form using these integers.

$(x - 1) (x + 2) = 0$

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

$x - 1 = 0$

$x + 2 = 0$

Set $x - 1$ equal to $0$ and solve for $x$ .

Set $x - 1$ equal to $0$ .

$x - 1 = 0$

Add $1$ to both sides of the equation.

$x = 1$

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.

$x = - 2$

The final solution is all the values that make $(x - 1) (x + 2) = 0$ true.

$x = 1, - 2$

The final solution is all the values that make $(x^{2} - 9) (x^{2} + x - 2) = 0$ true.

$x = 3, - 3, 1, - 2$

x-intercept(s) in point form.

x-intercept(s): $(3, 0), (- 3, 0), (1, 0), (- 2, 0)$

Step 2

Find the y-intercepts.

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

$y = ({(0)}^{2} - 9) ({(0)}^{2} + 0 - 2)$

Solve the equation.

Remove parentheses.

$y = ({(0)}^{2} - 9) ({(0)}^{2} + 0 - 2)$

Remove parentheses.

$y = (0^{2} - 9) ({(0)}^{2} + 0 - 2)$

Remove parentheses.

$y = (0^{2} - 9) (0^{2} + 0 - 2)$

Remove parentheses.

$y = ({(0)}^{2} - 9) ({(0)}^{2} + 0 - 2)$

Simplify $({(0)}^{2} - 9) ({(0)}^{2} + 0 - 2)$ .

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

$y = (0 - 9) ({(0)}^{2} + 0 - 2)$

Subtract $9$ from $0$ .

$y = - 9 ({(0)}^{2} + 0 - 2)$

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

$y = - 9 (0 + 0 - 2)$

Add $0$ and $0$ .

$y = - 9 (0 - 2)$

Subtract $2$ from $0$ .

$y = - 9 \cdot - 2$

Multiply $- 9$ by $- 2$ .

$y = 18$

y-intercept(s) in point form.

y-intercept(s): $(0, 18)$

Step 3

List the intersections.

x-intercept(s): $(3, 0), (- 3, 0), (1, 0), (- 2, 0)$

y-intercept(s): $(0, 18)$

Step 4

Find the x and y Intercepts p(x)=(x^2-9)(x^2+x-2)

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