Before moving further, we should quickly recap the terms constants, variables, polynomials & the terms in a polynomial. Also, what is the power of a variable? A constant in Algebra is a value which is fixed; while a variable does not have a fixed value, its value keeps varying. Now, when we combine the variables & constants with the help of the mathematical operators of multiplication & ‘/’ or division, we get some terms in algebra. These terms put together using addition & subtraction give us the polynomials. A polynomial may have any number of variables & constants, which may even be zero. This means that a polynomial may have only variables or even constants only. Example: 2 is a monomial, i.e., an expression with only 1 term. Also, xy is a monomial.
Now, to arrange polynomials in descending order, we consider any one of the variables in the polynomial & based on the power of that variable in each of the terms of the given polynomial, we arrange the terms in descending order.
Example: To arrange a polynomial 2x3 + 3 – 6yx + 7x2 + 9x – 12 + 5x4 , we take the variable ‘x’ & find that the terms of the polynomial are 2x3, 3, – 6yx, 7x2, 9x, – 12, 5x4 . Now we will compare the power of x in different terms & arrange the terms in decreasing order of the powers. So, the sequence of terms in such a decreasing order will be 5x4, 2x3, 7x2, – 6yx, 9x, 3, -12. Thus, the polynomial arranged in decreasing order will be given as 5x4 + 2x3 + 7x2 – 6yx + 9x + 3 - 12.