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Partial Fractions: Repeat & Non-Linear Factors

These are the harder decomposition with exponents in the denominator. Not so much harder, just more rules to remember and/or not screw up. Instead of just "A" and "B" in the numerators, you'll end up with stuff like "Ax+B", except when you don't. Makes sense, right?

This video appears on the page: Integration by Partial Fraction Decomposition ,Partial Fractions

Partial Fractions with "Non-Repeated Linear Factors"

That's a mouthful, no? This is the "easier" type of partial fraction decomposition problem where the denominator can be factored completely into stuff where there aren't any x2's -- or any other exponents -- anywhere in the denominator. I highly recommend you practice these before doing the next video.

This video appears on the page: Integration by Partial Fraction Decomposition ,Partial Fractions

Partial Fraction Decomposition
Partial Fractions with "Non-Repeated Linear Factors"
Partial Fractions: Repeat & Non-Linear Factors

In this chapter we'll learn a somewhat tedious process of splitting up a perfectly good rational expression into a couple fractions with A's and B's in the numerator.

Part of the course(s): Math Analysis ,College Algebra ,Pre-Calculus

Polynomial Inequalities

Not so different from the quadratic inequalities of the previous video, just more spots on number line! Plus, since there's more factors to play with (as your egghead teacher might say), they can pull some fun (their word) and/or mean tricks (mine) with exponents and repeated roots.

This video appears on the page: Rational & Polynomial Inequalities

Rational Inequalities

What happens when you put two polynomials above each other in an inequality? Believe it or not, it's not that much worse than if there was no fraction, just gotta be careful with open dots! (For a refresher on finding common denominators when x's and x2's are involved, check out my solving rational equations video.)

This video appears on the page: Rational & Polynomial Inequalities

Rational & Polynomial Inequalities
Quadratic Inequalities
Polynomial Inequalities
Rational Inequalities

In this chapter we'll return to the Big Three of inequalities -- number lines, test points, and interval notation -- for perhaps the final time (nostalgic yet?).

Part of the course(s): Math Analysis ,College Algebra ,Pre-Calculus

Rational Function Graphing Examples

In this video I work a couple of full-length rational function problems like the worst you might have on the test. We'll find: vertical asymptotes, holes, horizontal asymptotes, X- & Y-intercepts, domain, range, and we'll even draw the graphs!

This video appears on the page: Graphing Rational Functions

Slant Asymptotes (a.k.a. Oblique Asymptotes)

On the down side, these involve polynomial long division. On the up side, many teachers don't even cover this sub-topic, so check your syllabus! (If you don't remember polynomial long division, check out my polynomial division chapter.)

This video appears on the page: Graphing Rational Functions ,Inflection Points & Curve Sketching

Horizontal Asymptotes

Horizontal asymptotes come down to three simple rules that you'll just have to memorize, but most students don't have too much trouble with that. Key is that equations of horizontal lines are always y = number, so don't get confused and use x!

This video appears on the page: Graphing Rational Functions

Vertical Asymptotes & Holes

The most important thing about rational functions is that you're never ever allowed to divide by zero (those values aren't in domain); hence, the first thing we'll do in every problem is set the denominator equal to zero. Which zero is a vertical asymptote and which is a hole? What's a hole? And how can an asymptote be friendly or unfriendly? Stay tuned.

This video appears on the page: Graphing Rational Functions ,Inflection Points & Curve Sketching

Graphing Rational Functions
Vertical Asymptotes & Holes
Horizontal Asymptotes
Slant Asymptotes (a.k.a. Oblique Asymptotes)
Rational Function Graphing Examples

Rational functions bring with them a crazy list of math terms: asymptotes (horizontal, vertical, oblique & slant), domain, range, and intercepts. You're welcome.

Part of the course(s): Math Analysis ,College Algebra ,Pre-Calculus

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!

This video appears on the page: Polynomials & Rational Zeros

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.)

This video appears on the page: Polynomials & Rational Zeros

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!

This video appears on the page: Polynomials & Rational Zeros

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

This video appears on the page: Polynomials & Rational Zeros

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

This video appears on the page: Polynomials & Rational Zeros

Polynomials & Rational Zeros
Polynomial Graphs: Zeros, Multiplicity, End Behavior, Fundamental Theorem of Algebra
Complex & Imaginary Roots of Polynomials
Getting Equation From Roots
Finding Rational Roots of Polynomials
Calculator Tricks For Polynomials

In this chapter we'll put our synthetic division skills to the test by using "p/q" to fully factor higher-power polynomials containing x3, x4 and x5. Plus calculator graphing tips!

Part of the course(s): Math Analysis ,College Algebra ,Pre-Calculus

Synthetic Division

In this one we get to a shortcut technique for dividing polynomials: synthetic division. This shortcut only works for dividing in factors with an exponent of 1, such as "x-2" or "x+6", but that's what you usually have to do in this class. Yay! Synthetic division is also used for the Remainder Theorem.

This video appears on the page: Synthetic & Long Division of Polynomials

Polynomial Long Division

In this video I cover how to divide polynomials the same way you would have divided 14 into 159 in grammar school. The long way. Want to divide x3-1 into 5x5-3x4+3x-1? You came to the right place.

This video appears on the page: Synthetic & Long Division of Polynomials

Synthetic & Long Division of Polynomials
Polynomial Long Division
Synthetic Division

In this chapter we'll learn a somewhat tedious process of dividing polynomials by each other, a skill that's kind of fun once you get the hang of it and which will serve you well in Pre-Calc & Analysis.

Part of the course(s): Math Analysis ,College Algebra ,Algebra 2 ,Pre-Calculus