Three Trigonometric Inequalities

(A new question of the week) We often solve basic trigonometric equations; but a recent set of questions dealt with challenging trigonometric inequalities, which bring with them a new set of issues. We’ll look at several of those here, which combine trig with polynomials, rational functions, and more. Each will illustrate something new to watch …

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Advanced Logarithm Problems

(A new question of the week) Here is an interesting collection of problems involving logarithms with different bases, which require some unique thinking. And after we’d worked out a good strategy, another problem arose at a whole new level.

A Composite Quartic Equation

A question just after we recently discussed quartic equations, has special features that lead to a unique solution method. We’ll be showing how to use synthetic division, and seeing some interesting graphs.

Factoring a Quartic Polynomial

Factoring a quadratic polynomial (degree 2) is a standard topic in algebra; but for higher degrees, things get a lot harder. Here we’ll look at some old questions from the Ask Dr. Math site about factoring quartic (degree 4) polynomials. There is no standard method, but several interesting tricks you might want to know about.