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POLYNOMIAL IN ONE VARIABLE

**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’.**