Find the x and y Intercepts f(x)=(x^2-2x-8)/(3x-2)

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 ${\displaystyle -8}$ and whose sum is ${\displaystyle -2}$.

Write the factored form using these integers.

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

Add ${\displaystyle 4}$ to both sides of the equation.

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

Subtract ${\displaystyle 2}$ from both sides of the equation.

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

Multiply ${\displaystyle -2}$ by ${\displaystyle 0}$.

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

Subtract ${\displaystyle 8}$ from ${\displaystyle 0}$.

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

Subtract ${\displaystyle 2}$ from ${\displaystyle 0}$.