TopA polynomial is made from two terms ‘poly’ + ‘nomial’. Poly means many and ‘nomial’ means terms. So we can say that an expression with many terms is called as a polynomial. A polynomial is on the whole a mixture of constant terms and variables. 3x + y is polynomial because it consists of two terms 3x and y. Now consider if 2x + 3x is a polynomial. We can write 2x + 3x as 5x and we know that 5x is a monomial.
Thus 2x + 3x is indeed a monomial. So variable should be different with the entire constants. The degree of any polynomial is represented by highest power on its variables, if we are having a polynomial like x2+ 3x + 4, as we can see that highest power on the variable is two so the degree for the given polynomial is 2. And if we talk about 4th degree polynomial then it can be defined as the polynomial which is having the highest degree as 4, is a fourth degree polynomial. If we take a simple example as x4 + 3x3 + 2x2 + 3x +1, then we can see that ‘x’ is having the highest power as four so we can say that it is a fourth degree polynomial. If we take another example x4y4 + 3xy +8 then in this on ‘x’ as well as on ‘y’ the power is same.
As in the above case the highest power is on both so the degree of the polynomial will be four. Degree is just related to the highest power of the given polynomial. If we talk about 4th degree polynomial then we can perform any type of operation like addition, division, multiplication and subtraction. We can also factorize the fourth degree polynomial. This is all about fourth degree polynomial.