Look at these three expressions:

#1 :

#2 :

#3 :

They are all different representations of the same thing. The second expression is the expanded form of the first. It's called a "quadratic quadrinomial". The third simplifies it by combining the 8x and 3x, but the third is called a "quadratic trinomial". So even though they're both the same thing, they have different names. A few questions...

1. A polynomial is an expression with the 4 arithmetic operations and non-negative exponents. I usually see polynomials as a+b+c+d... etc. where a, b, c, d ... are the terms.Is the first expression above, , a polynomial?I'm not sure, since instead of the usual a+b+c+d..., the most precedent operation is multiplication, not addition.

2. If I expand the first expression, I get the second expression. However, it can be simplified by combining the 8x and 3x, making the third expression. The second is a quadratic quadrinomial, but the third is a quadratic trinomial. Even though they both represent the same thing, they have different names. This leads me to think that, in general, polynomials with different namescan(can, not will) essentially be the same thing as long as the highest degree is the same, e.g. a cubic trinomial and a cubic monomial (same degree, different # of terms). But not a cubic quadrinomial and a quadratic trinomial (because different degrees).Is this guessy inference I made true for all polynomials?