How to name the opposite of "leading term" in a polynomial?

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Any polynomial consists of many monomial terms. If we sort them by decreasing order according to the degree, then the first term is called the leading term. What about the last term? Is there a name for it?

For example, consider $x^5+2x^3-x^2$.

$x^5$ is called the leading term. I tend to call $5$ the leading degree. What to call $-x^2$? The "last term"? The "trailing term"? The "least term"? What about the number $2$? The "last degree"? etc.

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3 Answers

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There is no generally accepted term to denote the number you are referring to. In general, "trailing term" sounds nice, but it's nice if you explain what you mean by it (since some may understand that the trailing term of $x^2+x$ would be $0$, and others would understand it as $1$.

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I do not think there is a name for the lowest degree term. However, it is worth noting that there is a difference between "order" and "degree" of a polynomial. In your example, the degree of the polynomial is $5$, whereas the order of your polynomial is $2.$ In other words, the order of a polynomial is the "lowest power" with a non-zero coefficient.

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There is not a formal name for the term in this case. If it were a constant, we would call it the constant term. We may say that it is the term with degree 2, but there is no universal word for this term.

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