Find the x and y Intercepts (x^2+5x+4)/(2x^2-2)

$\frac{x^{2} + 5 x + 4}{2 x^{2} - 2}$

Write $\frac{x^{2} + 5 x + 4}{2 x^{2} - 2}$ as an equation.

$y = \frac{x^{2} + 5 x + 4}{2 x^{2} - 2}$

Find the x-intercepts.

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

$0 = \frac{x^{2} + 5 x + 4}{2 x^{2} - 2}$

Solve the equation.

Set the numerator equal to zero.

$x^{2} + 5 x + 4 = 0$

Solve the equation for $x$ .

Factor $x^{2} + 5 x + 4$ 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 $4$ and whose sum is $5$ .

$1, 4$

Write the factored form using these integers.

$(x + 1) (x + 4) = 0$

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

$x + 1 = 0$

$x + 4 = 0$

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 $x + 4$ equal to $0$ and solve for $x$ .

Set $x + 4$ equal to $0$ .

$x + 4 = 0$

Subtract $4$ from both sides of the equation.

$x = - 4$

The final solution is all the values that make $(x + 1) (x + 4) = 0$ true.

$x = - 1, - 4$

Exclude the solutions that do not make $0 = \frac{x^{2} + 5 x + 4}{2 x^{2} - 2}$ true.

$x = - 4$

x-intercept(s) in point form.

x-intercept(s): $(- 4, 0)$

Find the y-intercepts.

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

$y = \frac{{(0)}^{2} + 5 (0) + 4}{2 {(0)}^{2} - 2}$

Solve the equation.

Remove parentheses.

$y = \frac{0^{2} + 5 (0) + 4}{2 {(0)}^{2} - 2}$

Remove parentheses.

$y = \frac{0^{2} + 5 (0) + 4}{2 \cdot 0^{2} - 2}$

Remove parentheses.

$y = \frac{{(0)}^{2} + 5 (0) + 4}{2 {(0)}^{2} - 2}$

Simplify $\frac{{(0)}^{2} + 5 (0) + 4}{2 {(0)}^{2} - 2}$ .

Simplify the numerator.

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

$y = \frac{0 + 5 (0) + 4}{2 \cdot 0^{2} - 2}$

Multiply $5$ by $0$ .

$y = \frac{0 + 0 + 4}{2 \cdot 0^{2} - 2}$

Add $0$ and $0$ .

$y = \frac{0 + 4}{2 \cdot 0^{2} - 2}$

Add $0$ and $4$ .

$y = \frac{4}{2 \cdot 0^{2} - 2}$

Simplify the denominator.

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

$y = \frac{4}{2 \cdot 0 - 2}$

Multiply $2$ by $0$ .

$y = \frac{4}{0 - 2}$

Subtract $2$ from $0$ .

$y = \frac{4}{- 2}$

Divide $4$ by $- 2$ .

$y = - 2$

y-intercept(s) in point form.

y-intercept(s): $(0, - 2)$

List the intersections.

x-intercept(s): $(- 4, 0)$

y-intercept(s): $(0, - 2)$

Find the x and y Intercepts (x^2+5x+4)/(2x^2-2)

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