Dimensions and degree of an expression, Mathematics

Binomials, Trinomials and Polynomials which we have seen above are not the only type. We can have them in a single variable say 'x' and of the form x2 + 4x2 - 5x + 1. Before we go into these, first let us understand what is meant by dimension. It is defined as each of the letters (symbols) comprising a term. That is, in term abc, a, b and c are the three letters which indicate that the dimension is 3. Compared to this we define degree as number of letters in a term. The number of letters in the term abc are 3 and therefore, it can be said that it is of 3rd degree. You find these two somewhat similar. However, the degree of an expression consisting of two or more terms is of that term which has the highest dimension. That is, in an expression 6a3x3 + 5b2x5 - 3c2x2, we find that the dimensions of the term 6a3x3 is 6, that of the term 5b2x5 is 7 and that of the term 3c2x2 is 4. The degree of this expression is, therefore, 7. An expression in which the terms have same dimensions is said to be a homogeneous expression. The like and unlike terms which we have seen earlier is at the most of two degrees. We do have terms of higher degrees also. An expression of the form 3x5 + 7x4 + x3 - 2x + 5 is of degree 5. In polynomials we deal with expressions like these. In this part first we look at their addition, subtraction and multiplication. In case of division, we will list the steps and look at a couple of examples involving binomials before we go to polynomials. In the later part we look at how to factorize expressions of any given degree.

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