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

$f (x) = (x^{2} - 4) (3 - x)$

Step 1

Find the x-intercepts.

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

$0 = (x^{2} - 4) (3 - x)$

Solve the equation.

Rewrite the equation as $(x^{2} - 4) (3 - x) = 0$ .

$(x^{2} - 4) (3 - x) = 0$

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

$x^{2} - 4 = 0$

$3 - x = 0$

Set $x^{2} - 4$ equal to $0$ and solve for $x$ .

Set $x^{2} - 4$ equal to $0$ .

$x^{2} - 4 = 0$

Solve $x^{2} - 4 = 0$ for $x$ .

Add $4$ to both sides of the equation.

$x^{2} = 4$

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

$x = \pm \sqrt{4}$

Simplify $\pm \sqrt{4}$ .

Rewrite $4$ as $2^{2}$ .

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

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

$x = \pm 2$

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.

$x = 2$

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

$x = - 2$

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

$x = 2, - 2$

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

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

$3 - x = 0$

Solve $3 - x = 0$ for $x$ .

Subtract $3$ from both sides of the equation.

$- x = - 3$

Divide each term in $- x = - 3$ by $- 1$ and simplify.

Divide each term in $- x = - 3$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 3}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 3}{- 1}$

Divide $x$ by $1$ .

$x = \frac{- 3}{- 1}$

Simplify the right side.

Divide $- 3$ by $- 1$ .

$x = 3$

The final solution is all the values that make $(x^{2} - 4) (3 - x) = 0$ true.

$x = 2, - 2, 3$

x-intercept(s) in point form.

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

Step 2

Find the y-intercepts.

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

$y = ({(0)}^{2} - 4) (3 - (0))$

Solve the equation.

Remove parentheses.

$y = (0^{2} - 4) (3 - (0))$

Remove parentheses.

$y = ({(0)}^{2} - 4) (3 - (0))$

Simplify $({(0)}^{2} - 4) (3 - (0))$ .

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

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

Subtract $4$ from $0$ .

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

Subtract $0$ from $3$ .

$y = - 4 \cdot 3$

Multiply $- 4$ by $3$ .

$y = - 12$

y-intercept(s) in point form.

y-intercept(s): $(0, - 12)$

Step 3

List the intersections.

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

y-intercept(s): $(0, - 12)$

Step 4

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

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