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.
Negative vs Minus: Two Words, One Symbol?
Last time we looked into terminology related to negative numbers; one subtopic was too big to fit, so I’ve broken it out into a separate post. How are the concepts of “negative” and “minus” (subtraction) related? How much do we need to distinguish them? We’ll look at two questions, the first from a child focused …
Talking About Negative Numbers
Last week we looked at what negative numbers mean; here we’ll consider a number of questions we’ve been asked about the terminology of signed numbers: what “negative” means, and other words for negative numbers. Up, down, and opposite This question from 1998 asks about translating words to signed numbers: Converting Words to Numbers Can you …
How Real Are Negative Numbers?
This week we’ll look at some Ask Dr. Math questions like, “How can a number be less than zero?” and “Why do we need negative numbers?” We’ll see a number of examples of their use, and how negative numbers make life easier.
Subtleties of Inverse Trig Functions
(A new question of the week) It is not uncommon for students to ask about why they get different answers using different methods. Usually the answer is that the answers are really equivalent. This time, the answers really are different! This was partly the result of being taught an incomplete technique, omitting important cautions. And …
Factoring Tricks from an Old Textbook
(A new question of the week) Last week I discussed several Ask Dr. Math questions about factoring quartic polynomials, which had been on my list of potential topics. That list also included a question on that topic from three years ago, that didn’t make it into the blog at the time. That will lead us …
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.
A Tunnel Through the Earth
I have a very short problem this week: How deep will you go if you dig a straight tunnel through the earth, how long will it be, and what angle do you have to start at?
Combinatorics: Multiple Methods, Subtle Wording
(A new question of the week) With few new questions of general interest available this week, I thought I’d go back a few months to a couple little questions on a topic we haven’t dealt with lately, combinatorics. We’ll have one question each on permutations and combinations, showing some subtlety in both the methods we …
A Hole in a Cube
(A new question of the week) Here is an interesting little question about how drilling a hole affects volume and surface area. We’ll have one answer, and several explanations.