Find the x and y Intercepts (x^2+9x+20)/(x^2+25)

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 ${\displaystyle 20}$ and whose sum is ${\displaystyle 9}$.

Write the factored form using these integers.

Set ${\displaystyle x+4}$ equal to ${\displaystyle 0}$.

Subtract ${\displaystyle 4}$ from both sides of the equation.

Set ${\displaystyle x+5}$ equal to ${\displaystyle 0}$.

Subtract ${\displaystyle 5}$ from both sides of the equation.

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

Multiply ${\displaystyle 9}$ by ${\displaystyle 0}$.

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

Add ${\displaystyle 0}$ and ${\displaystyle 20}$.

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

Add ${\displaystyle 0}$ and ${\displaystyle 25}$.

Factor ${\displaystyle 5}$ out of ${\displaystyle 20}$.

Cancel the common factors.