Find the x and y Intercepts f(x)=(3x^2-192)/(x+5)

$f (x) = \frac{3 x^{2} - 192}{x + 5}$

Step 1

Find the x-intercepts.

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

$0 = \frac{3 x^{2} - 192}{x + 5}$

Solve the equation.

Set the numerator equal to zero.

$3 x^{2} - 192 = 0$

Solve the equation for $x$ .

Add $192$ to both sides of the equation.

$3 x^{2} = 192$

Divide each term in $3 x^{2} = 192$ by $3$ and simplify.

Divide each term in $3 x^{2} = 192$ by $3$ .

$\frac{3 x^{2}}{3} = \frac{192}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x^{2}}{3} = \frac{192}{3}$

Divide $x^{2}$ by $1$ .

$x^{2} = \frac{192}{3}$

Simplify the right side.

Divide $192$ by $3$ .

$x^{2} = 64$

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

$x = \pm \sqrt{64}$

Simplify $\pm \sqrt{64}$ .

Rewrite $64$ as $8^{2}$ .

$x = \pm \sqrt{8^{2}}$

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

$x = \pm 8$

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.

$x = 8$

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

$x = - 8$

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

$x = 8, - 8$

x-intercept(s) in point form.

x-intercept(s): $(8, 0), (- 8, 0)$

Step 2

Find the y-intercepts.

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

$y = \frac{3 {(0)}^{2} - 192}{(0) + 5}$

Solve the equation.

Remove parentheses.

$y = \frac{3 \cdot 0^{2} - 192}{(0) + 5}$

Remove parentheses.

$y = \frac{3 \cdot 0^{2} - 192}{0 + 5}$

Remove parentheses.

$y = \frac{3 {(0)}^{2} - 192}{(0) + 5}$

Simplify $\frac{3 {(0)}^{2} - 192}{(0) + 5}$ .

Simplify the numerator.

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

$y = \frac{3 \cdot 0 - 192}{0 + 5}$

Multiply $3$ by $0$ .

$y = \frac{0 - 192}{0 + 5}$

Subtract $192$ from $0$ .

$y = \frac{- 192}{0 + 5}$

Simplify the expression.

Add $0$ and $5$ .

$y = \frac{- 192}{5}$

Move the negative in front of the fraction.

$y = - \frac{192}{5}$

y-intercept(s) in point form.

y-intercept(s): $(0, - \frac{192}{5})$

Step 3

List the intersections.

x-intercept(s): $(8, 0), (- 8, 0)$

y-intercept(s): $(0, - \frac{192}{5})$

Step 4

Find the x and y Intercepts f(x)=(3x^2-192)/(x+5)

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