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.