Roots and Factors of Polynomials Part 2

​Now consider the following factors: Graph them in Desmos


(x - 5) (x - 5)² (x² - 5)

​Now try without the graphing....

​On the next slide....
Try graphing a 3rd degree polynomial in standard form with 4 terms.
Try making it have 3 integer roots.

​When the number is not a perfect square

set the factor = 0 and then solve for x

Ex: x² - 5 = 0 so x² = 5 square root both sides

x = +√5 and x = -√5 These are called conjugate irrational roots
**irrational roots ALWAYS come in pairs!!

​What if the factor is (x² + 9)?

What happens when you set the factor = to ZERO?
When you try to solve for x, what happens?

This is a future lesson, but you already have a head- start!!