Before going to know about Polynomials, we learn some Basics
Constant: All the numbers are called as Constants.
Constant term: A term having only number.
Term: A term is separated from other terms by "+ or -" symbols.
Variable: It is a symbol to represent an unknown value and it can take any real number as its value. Generally we use English alphbet to denote variables. (a, b, c, ,,,,,,,,,,x, y, z)
Variable term: The product of constant and variables.
Degree of variable term: The exponent of the variable is the degree of that term. ( If the term having more than one variable, the degree is the "sum of exponents of all variables")
Mathematical Expression: An expression is combination of numbers and mathametical operations(+, -, x, ÷, .........). This is also called Numerical Expression.
Algebraic Expression: If a numerical expression contains atleast one variable, it is called Algebraic expression.
Types of Algebraic Expressions:
1. MONOMIAL:
If an expression having only ONE term, it is called Monomial.
2. BINOMIAL:
If an expression having only TWO terms, it is called Binomial.
3. TRINOMIAL:
If an expression having only THREE terms, it is called Trinomial.
4. MULTINOMIAL:
If an expression contains more than three terms, it is called Multinomial.
POLYNOMIAL:
A Polynomial is an Algebraic epression which having Non-Negative integers as exponents of the variables.
NOTE:
1. An Algebraic epression is not a Polynomial, If a variable having negative integer as exponents.
2. An Algebraic epression is not a Polynomial, If a variable having fractions as exponents.
3. An Algebraic epression is not a Polynomial, If any variable involved in the denominator.
DEGREE OF A POLYNOMIAL:
Highest degree from all the degrees of terms of a Polynomial is called the Degree of Polynomial.
Types of Polynomials:
1. ZEROTH POLYNOMIAL:
ZERO is called ZEROTH POLYNOMIAL.
Its degree is not exist(Not Defined)
2. CONSTANT POLYNOMIAL:
Any number other than zero is called Constant polynomial
Its degree is "Zero"
3. LINEAR POLYNOMIAL:
A Polynomial having degree "ONE", is called Linear Polynomial.
Its degree is "ONE"
4. QUADRATIC POLYNOMIAL:
A Polynomial which has degree "TWO", is called Quadratic Polynomial.
Its degree is "TWO"
5. CUBIC POLYNOMIAL:
A Polynomial which has degree "THREE", is called Cubic Polynomial.
Its degree is "Three"
6. nth degree POLYNOMIAL:
A Polynomial which has degree "n", is called nth degree Polynomial.
Its degree is "n"