Polynomial in one Variable
An algebraic expression is called a polynomial in one variable if the literal factor of each of its terms is a power of the variable if the literal factor of each of its terms is a power of the variable. Such an expression can, of course, contain a constant term. The power of the variable in the constant term is zero ‘0’, as a⁰ = 1, thus a polynomial in the variable ‘a’ can have constants and the power of x, such as a, a², aᶟ, a⁴, a⁵, a⁶,……...
The highest power of the variable appearing in any of the terms of the polynomial is called the degree of the polynomial. As an example, we can observe that –
1) We can find here, 5a + 3 is a polynomial in ‘a’, the degree of the polynomial is 1. There are two terms in the polynomial.
2) As we can find here, 3a²+ 4a - 6 is a polynomial in ‘a’ of degree 2. The indices of the powers of ‘a’ in the three terms are 2, 1, & 0 respectively.
3) We can find here, 7b⁵- 3/5 b²+ 7b is a polynomial in ‘b’ of degree 5.
4) We can observed here, 3a⁴ + 7/a² + 8a is not polynomial.
5) We can observed here, 4/a⁵ - 4a² + 2/7 is not a polynomial.
6) We can observe here, a⁸ + 5ab² + 7b⁵ is a polynomial in two variables ‘a’ & ‘b’.