Find the Roots (Zeros) (x^2+3x-18)/(x+9)

$\frac{x^{2} + 3 x - 18}{x + 9}$

Set $\frac{x^{2} + 3 x - 18}{x + 9}$ equal to $0$ .

$\frac{x^{2} + 3 x - 18}{x + 9} = 0$

Solve for $x$ .

Set the numerator equal to zero.

$x^{2} + 3 x - 18 = 0$

Solve the equation for $x$ .

Factor $x^{2} + 3 x - 18$ 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 $- 18$ and whose sum is $3$ .

$- 3, 6$

Write the factored form using these integers.

$(x - 3) (x + 6) = 0$

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

$x - 3 = 0$

$x + 6 = 0$

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

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

$x - 3 = 0$

Add $3$ to both sides of the equation.

$x = 3$

Set $x + 6$ equal to $0$ and solve for $x$ .

Set $x + 6$ equal to $0$ .

$x + 6 = 0$

Subtract $6$ from both sides of the equation.

$x = - 6$

The final solution is all the values that make $(x - 3) (x + 6) = 0$ true.

$x = 3, - 6$

Find the Roots (Zeros) (x^2+3x-18)/(x+9)

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