A polynomial is a mathematical expression that consists of several components, or terms, containing both numerical and literal symbols and connected by addition. An essential rule of a polynomial is that all its parts cannot be added, which means that the polynomial is already represented in the simplest form. Thus, depending on the number of independent terms in a polynomial, there are monomials (1), binomials (2), and trinomials (≥3).
For the same reason, adding a zero to a polynomial does not modify it. As a result, it remains unchanged. Also, it is worth noting that the terms whose literal parts are identical can be added. Moreover, in the case of replacing terms with literal symbols, nothing will change. The most significant power in the polynomial is the total power of the polynomial. It is then appropriate to say that when performing addition or subtraction, all arithmetic operations are performed strictly between the related terms, whereas for multiplication or division, it does not matter.
(x^2+x)+(2x^2+3x)=(x^2+2x^2 )+(x+3x)=3x^2+4x [1]
(x^2+x)(2x^2+3x)=2x^2 x^2+x^2 3x+x2x^2+x3x=2x^4+5x^3+3x^2 [2]