MHB Understand Polynomial Terms: Like & Unlike Terms

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Like terms in polynomials are defined as terms that share the same variable and exponent, while unlike terms do not. For example, in the polynomials 3x^2 + 2x - 3 and 5x^3 - 3x + 7, the only like term is the x term, as it appears in both polynomials. The discussion also touches on the idea of constant terms being considered like terms since they can be represented as x^0, though this is not commonly accepted. Understanding these concepts through the lens of set theory can help clarify the relationships between terms in polynomials. Overall, grasping the distinction between like and unlike terms is essential for working with polynomials effectively.
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I would like to have someone who would be willing to explain me what is a like term and an unlike term in terms of set theory. I'm just an high-scool student, but I really would like to understand it from that point of view anyway. It doesn't have to be a 1000 pages long of explanations.
 
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PeekaTweak said:
I would like to have someone who would be willing to explain me what is a like term and an unlike term in terms of set theory. I'm just an high-scool student, but I really would like to understand it from that point of view anyway. It doesn't have to be a 1000 pages long of explanations.
In terms of polynomials (I can't think of how to applied this to sets) a "like" term is a comparison between two terms of the polynomial. For example, consider the two polynomials [math]3x^2 + 2x - 3[/math] and [math]5x^3 - 3x + 7[/math]. The like terms are the terms that are in both polynomials. Here the there is only one like term: the one in x. (I suppose you could call the constant terms "like" as they are both terms in [math]x^0[/math] but I don't think anyone does this.)

-Dan
 

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