Polynomials: A Matter of Degrees
Last time we examined why polynomials are defined as they are. This time, let’s look at some tricky aspects of the concept of “degree”, mostly involving something being zero.
Polynomials: Why Are Terms What They Are?
A question last week (Hi, Zahraa!) led me to dig up some old discussions of how we define a polynomial (or monomial, or term) and, specifically, why the exponents have to be non-negative integers. Why can we only multiply, and not divide by, variables? Since we’ve been looking at polynomials, let’s continue.
The Shape of a Polynomial at its Zeros
Last week’s discussion about zeros of a polynomial, and other conversations, have reminded me of a past discussion of the shape of the graph of a polynomial near its zeros. Let’s take a look, starting with some other questions that nicely lead up to it.
Why Proof Matters: Polynomial Zeros and Turning Points
A recent question from a student demonstrates that not everything on the Internet should be taken at face value – and that it’s easy to think you are right when you are not.
Intersecting Powers and Roots
Here is an interesting little question. Its answer is simple, and not hard to see just by graphing examples; yet the algebra is easy to get wrong, as we’ll see several times. And subtle errors deserve study.
Boxes, Whiskers, and Outliers
Last week we looked at one way to display data, the stem-and-leaf plot. This time, we’ll look at a very different one, the box-and-whisker plot, which summarizes the data more broadly.
Stems, Leaves, and Data
It’s been a while since we’ve written about statistics, so I want to start a short series about that. Here, we’ll look into stem-and-leaf plots (also called stemplots).
Adjoints and Inconsistency: A Questionable Test
(A new question of the week) Last week we looked at how the adjugate matrix can be used to find an inverse. (This was formerly called the [classical] adjoint, a term that is avoided because it conflicts with another use of the word, but is still used in many sources.) I posted that as background …
Determinants, Adjugates, and Inverses
(A new question of the week) Looking for a new topic, I realized that a recent question involves determinants, and an older one provides the background for that. We’ll continue the series on determinants by seeing how they can be used in finding the inverse of a matrix, and how something called the adjugate matrix …
How Can 3×3 Determinants Give Both Area and Volume?
(A new question of the week) A recent question asked for the connection between two different ways to use determinants geometrically: to find the area of a triangle, and to find the volume of a pyramid (or the area of a parallelogram and the volume of a parallelepiped). Last time we looked at what a …
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