Find the zeros of polynomial functions and solve polynomial equations.

f (x) = x^3-5x^2-9x+45

Find the zeros, just equal the equation to 0.

x³ - 5x² - 9x + 45 = 0

Factor:

x². (x - 5) - 9. (x - 5) = 0

(x² - 9). (x - 5) = 0

It's a multiplication, so, if one term goes to 0, everything goes too.

x² - 9 = 0

x² = 9

x = + or - √9

x' = 3

x'' = - 3

x - 5 = 0

x = 5

Now we have three roots: - 3, 3, 5.