How do you factor #r^3 - 2r^2 - 5r + 6 = 0#?
Using the rational root theorem, you can deduce that the possible roots of the function are
Now, just plug in some of the possible roots into the equation to see if it equals
Now that we have determined a root of the original equation, we can use synthetic division to divide the polynomial by the binomial
Now it is simply factoring quadratic equation. When we factor, we get
Combining these roots with our roots determined earlier, we can get the full answer as