# #11149

00

Nov. 14, 2022, 1:38 p.m.

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//the next class from 11132 Schwartz: If you want to plug in 2 to a polynomial, you can do that. Schwartz: Just construct the polynomial ring, and mod it out by the ideal generated by x - 2! Michael: Will this be on the test?

it will not, but you should learn about it anyway because it's cool

# #9181

810

Sept. 15, 2021, 4:22 p.m.

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// discussing Law of Ones Schwartz: What do you do when none of 0, 1, -1, 2, -2 are roots of the polynomial? // students suggest things like Rational Root Theorem Schwartz: You cry! You cry before you try something like the Rational Root Theorem!

cf 8676

# #5319

1414

Dec. 15, 2014, 7:59 p.m.

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//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?