# Tag Info

### How can we best motivate the study of polynomials to high-school students?

Using puzzles to attract attention: "Think of a number, subtract 7, multiply 3, add 30, divide by 3. Then subtract the original number. The result will always be 3. Why does this magic work?"...
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### Are degrees of polynomials illogically defined in elementary algebra, intermediate algebra and college algebra courses?

I'm going to rewrite this answer to clarify what I think the issue is. I think the OP is imagining a different definition of the ring $k[x]$ than most answerers are. Here are two reasonable ...
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### Where do students learn to solve polynomial equations these days?

Students learn linear and quadratic equations in high school algebra. And then, if they have forgotten it, re-learn it in college, in courses called "pre-calculus" or something. Unless they ...
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### Non-US polynomial division notation

In Greece the students are taught polynomial division in the second class of upper high school (grade 11 at US educational system). It is the same algorithm as in Italy and Russia. Whole book in pdf ...
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### Non-US polynomial division notation

In Italy, polynomial long division is usually presented as in the following example taken from one of the most widely used textbooks for first year high school students (M. Bergamini, G. Barozzi, A. ...
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Accepted

### Non-US polynomial division notation

Here is a Russian 7th grade algebra textbook (publisher's website). Attached is a complete section dedicated to polynomial division, it is marked as optional.
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Accepted

### Where do students learn to solve polynomial equations these days?

The rational root theorem, synthetic division, the remainder theorem, Descartes rule of signs, and similar lower level topics were fairly widely taught in U.S. high school algebra-2 courses before and ...
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### Is the constant term a coefficient?

Your question is kind of two parts: one about a convention Is the constant term a "coefficient" and one about a philosophy, which I perhaps find to be a more important question to answer. Isn'...
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### Where do students learn to solve polynomial equations these days?

In the United States, solving linear and quadratic equations is a standard part of Algebra 1, which most students take in 8th or 9th grade. Students will return to polynomials and see long division ...

### Are degrees of polynomials illogically defined in elementary algebra, intermediate algebra and college algebra courses?

This: "On the other hand, without the proof the definition of the degree of polynomials is not even logically established." is not quite right. What is needed to establish the definition is the fact ...
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### Definition of equation vs. expression vs. polynomial

Here are informal definitions of the terms that seem confusing to you: A function is a relation between two sets, usually sets of numbers. It maps elements of the first set to elements of the second ...
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### How can we best motivate the study of polynomials to high-school students?

If the student has ever used a vector-based computer drawing program, they will be familiar with Bézier curves. Bézier curves are extremely intuitive to understand for humans. They became popular as a ...
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### Is coefficient same as constant?

I'd say that the video is not using the best word. I would call that constant the coefficient. Constant means that it is a number and not a variable. That's true. But the word coefficient conveys more ...
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### Improving exposition of a proof about polynomials over infinite fields

How about this: Let $k$ be an infinite field, and let $f \in k[x]$. Assume $f(t) = 0$ for all $t \in k$. Assume to the contrary that $f$ is not the zero polynomial. Then $f$ is a polynomial of ...
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### Is the constant term a coefficient?

It sometimes happens that slightly different definitions of the same word each have advantages and disadvantages. In such cases, I wouldn't be surprised to see some people supporting one definition ...
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### Is the constant term a coefficient?

I have to admit I was skeptical of the OP's claim that contemporary textbooks do not identify the constant term as a coefficient, so I checked the first book that I had handy -- and indeed it does ...
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### Where do students learn to solve polynomial equations these days?

Synthetic division is a standard part of the stereotypical "algebra 2" course in the US (~grade 11) and is normally covered including drill problems and examination. In my experience, cubics and ...
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### How can we best motivate the study of polynomials to high-school students?

if you're willing to take a bit of diversion, you could show how polynomials are used for error correcting codes that make the internet possible (reed-Solomon, but do it with real numbers instead of ...
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### How can we best motivate the study of polynomials to high-school students?

I disagree with the claim by others that puzzles are more applicable to top students than struggling ones. Of course, you must choose the right puzzles for the right level, and actually teach them how ...
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