TopLet ‘x’ be a variable, n be a positive Integer and as a1, a2,......an be a constant then,
f(x)= anxn+an-1xn-1+ ….+ a1x+a0
This expression is called a polynomial with variable ‘x’. Here ‘a0’ is the first term of the polynomial and x, x1 ….. are the variables for example 3x-2 is polynomial with variable ‘x’, 3y2-2y + 4 is a polynomial with variable ‘y’. If we put the value of ‘x’ as zero in the above expression then we will get the term ‘a0’. And we know that ‘a0’ is a monomial so if we put the value of variable as zero then polynomial becomes a monomial.
Now we will move to degree of Polynomials. Degree of polynomial is the exponent of highest degree in a polynomial is known as its degree. In other words we can say that the highest power of ‘x’ in a polynomial f(x) is called degree of the polynomial f(x).
If we take an example of a polynomial as 3x+1 then it is a polynomial in the variable x of degree 1, 2y2 + 3y -1 is a polynomial in the variable of degree 2, 4y5 + 6y4 +4y3 + 3y2 + 3y + 1 is a polynomial in the variable of degree 5. it can also happen that we are given a polynomial like 4x3y3 + 3x2 + 4x +2 , and we are asked to find the degree of the polynomial , there is no need to be getting confused we need to concentrate on the highest power on the variable that is three for the above problem so degree will be three. The polynomial with degree one is called as linear polynomial, the polynomial with degree two are called as quadratic polynomial, the polynomial with degree three are called as cubic polynomial and polynomial with degree four are bi- quadratic polynomial.