Find the x and y Intercepts r(x)=(x^2+5x-14)/((x+1)(x-3)(x+7))

Consider the form ${\displaystyle x^2+bx+c}$. Find a pair of integers whose product is ${\displaystyle c}$ and whose sum is ${\displaystyle b}$. In this case, whose product is ${\displaystyle -14}$ and whose sum is ${\displaystyle 5}$.

Write the factored form using these integers.

Set ${\displaystyle x-2}$ equal to ${\displaystyle 0}$.

Add ${\displaystyle 2}$ to both sides of the equation.

Set ${\displaystyle x+7}$ equal to ${\displaystyle 0}$.

Subtract ${\displaystyle 7}$ from both sides of the equation.

Raising ${\displaystyle 0}$ to any positive power yields ${\displaystyle 0}$.

Multiply ${\displaystyle 5}$ by ${\displaystyle 0}$.

Add ${\displaystyle 0}$ and ${\displaystyle 0}$.

Subtract ${\displaystyle 14}$ from ${\displaystyle 0}$.

Add ${\displaystyle 0}$ and ${\displaystyle 1}$.

Multiply ${\displaystyle 0-3}$ by ${\displaystyle 1}$.

Subtract ${\displaystyle 3}$ from ${\displaystyle 0}$.

Add ${\displaystyle 0}$ and ${\displaystyle 7}$.

Multiply ${\displaystyle -3}$ by ${\displaystyle 7}$.

Cancel the common factor of ${\displaystyle -14}$ and ${\displaystyle -21}$.