//Functions, first period. Descartes Law of Signs and Upper Bound of Roots Theorem. Rose has just used synthetic division with 5 on a polynomial and ended up with a nonzero remainder. Rose: Oh no! 5 is not a real root! But, class, you see, dividing by a number that is not a root is a lot like a break-up: You could just rush on blindly looking for the next opportunity, or you could slow down and consider the implications, and why everything went wrong... So what does anyone notice about the remainder? Noah Kim: Wait, Mr. Rose, is this related to your personal experience? //a little bit later, talking about graphs of polynomials in relation to roots Rose: But we know what graphs of polynomials look like! They're so continuous and smooth and predictable.... Noah Kim: Mr. Rose, you are still talking about math, right?
//completing the square to get the quadratic formula Rose: Try to contain your excitement. Student: Oh my god I'm so excited I think I might throw up! Rose: Cool.