The term "Polynomial" means "equation with crazy powers of x" like x3, x4 and x5. In this chapter we'll put our synthetic division skills to the test by using "p/q" to fully factor these high-power nightmares. If you're one of the lucky few who get to use calculators in this chapter, the last video is for you! (If you don't get to use calculators, don't look. It's too wonderful.)
Polynomial Graphs: Zeros, Multiplicity & End Behavior
In this video I cover everything you'll need to graph a polynomial once it's been factored: "end behavior" of graphs (which way the arrows point); number of real zeros; and what the heck "multiplicity" means and how it's gonna mess with the x-intercepts on your graph. Includes Fundamental Theorem of Algebra N.CN.9
Complex & Imaginary Roots of Polynomials
In this video I introduce complex roots to the graphing process, which is obviously going to be a bit strange since it's not like "3i" is on the x-axis.N.CN.9
Getting Equation From Roots
This video covers a very specific type of burn problem that every teacher puts on their test for the polynomials chapter. The problem: "Find a polynomial function of least degree with rational coefficients and roots of 1, -1, and 2i." The burn? Just watch!
Finding Rational Roots of Polynomials
Finally, we're ready to factor higher-order polynomials using synthetic division and "p/q" (if you've had this in class, you know what I'm talking about). (If you're not sure about Synthetic Division, check out my polynomial division chapter.)
Calculator Tricks For Polynomials
In West L.A. where I tutor, it seems like most teachers don't let kids use graphing calculators on tests where they'd actually be useful. But if you're in that lucky minority who gets to use calculators, this video is for you. Lots less synthetic division to do when finding roots of polynomials!
If you do not have an account, you should get one, because it is awesome! You can save a playlist for each test or each chapter, and save your "greatest hits" into a "watch right before the final" list (not that we recommend cramming, but when in Rome...)