Find the Roots (Zeros) (x^2+6x+8)/(x+4)

$\frac{x^{2} + 6 x + 8}{x + 4}$

Set $\frac{x^{2} + 6 x + 8}{x + 4}$ equal to $0$ .

$\frac{x^{2} + 6 x + 8}{x + 4} = 0$

Solve for $x$ .

Set the numerator equal to zero.

$x^{2} + 6 x + 8 = 0$

Solve the equation for $x$ .

Factor $x^{2} + 6 x + 8$ 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 $8$ and whose sum is $6$ .

$2, 4$

Write the factored form using these integers.

$(x + 2) (x + 4) = 0$

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

$x + 2 = 0$

$x + 4 = 0$

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.

$x = - 2$

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 $(x + 2) (x + 4) = 0$ true.

$x = - 2, - 4$

Exclude the solutions that do not make $\frac{x^{2} + 6 x + 8}{x + 4} = 0$ true.

$x = - 2$

Find the Roots (Zeros) (x^2+6x+8)/(x+4)

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