Discussion:  All Lesson Plans in Algebra 
Topic:  What is a binomial? 
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Subject:  What is a binomial? 
Author:  Eric Goolish 
Date:  Apr 29 2005 
what is a binomial?
The resources I have suggest a binomial is a polynomial, therefore it is the sum
of monomials, specially two monomials. However, there is no discussion of
simplified form.
So playing devil's advocate, is 5 + 2 a binomial? I don't think so because it
can be simplifed to 7, which is a monomial.
However, one textbook I use for class suggests that (a sqrt b) + (c sqrt d) is a
binomial. Specifically, they say BINOMIALS of the form (a sqrt b) + (c sqrt d)
and (a sqrt b)  (c sqrt d) are conjugates.
Personally, I feel these can be called binomials because there are two terms
when simplied. For instance, sqrt 2 + sqrt 3 (Binomial).
However, it can also be suggested that sqrt 2 + sqrt 3 is just one entity, one
number, so is it a monomial? Perhaps, (sqrt 2 + sqrt 3)x^0  representing the
degree of 0, thus a constant, thus a monomial?
What does everyone think about this? The more I dig into these math ideas, the
more I think there is much confussion in our notation and terminology. How can
1 + 1/2 be written as 1 1/2 (one and a half) with no addition sign, but now if
we have 2 + sqrt 3, we cannot put them together and write 2 sqrt 3 because that
would mean multiplication. I think there is much confusion here and we should
not be surprised when students 'don't get it.'
What does everyone think???
Eric Goolish (Curie Metro High Student Teacher)
 
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