Can single variables be called prime factors?

error_404

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Oct 13, 2021
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Hi guys! Prime factor decomposition of the term like 10y²z³ gives some prime numbers and single variables 2×5×y×y×z×z×z. In this example, 2 and 5 can be called prime factors, can't they? Can y and z be called prime factors also? If "no," is there one name suitable both for the prime numbers and single variables that we obtain after the prime factor decomposition?
 

Otis

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Apr 22, 2015
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Hi error_404. In the context of prime factors, I also think of symbols y and z as 'irreducible polynomials' or 'irreducible monomial factors'. In algebra, we refer to such polynomials as 'prime factors' of a source polynomial because they themselves cannot be factored, not because they represent prime numbers. (We wouldn't call y or z a prime number, without first knowing a specific value, as you seem to already understand.)

2x^2 - 2 = (2)(x + 1)(x - 1)

Those are three prime factors of the quadratic polynomial. The factor 2 is clearly a prime number, and we don't have enough information to know whether either of the irreducible binomial factors represent prime numbers yet they are prime factors in algebra.

Prime factors in algebra play a similar role as prime numbers do in arithmetic.

😎
 
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