Degree of a Term

The highest index of power or the sum of the indices of power of the variable(s) in a term is called the degree of the term.

Examples.1)  – 5 x⁴ is of the four degree

Examples.2)  the degree of the term a⁴b²c⁵d⁶ is  (4 + 2 + 5 + 6) =  17

Examples.3)  the degree of the term 8 x⁴yz⁵ is  (4 + 3 + 5) = 12

Example.4)   15 aˉ⁴b⁶c⁸ is a term of degree is  {(-4) + 6 + 8 } = 10


Polynomial in one Variable

An algebraic expression is called a polynomial if it is a finite sum of terms that contain only non-negative integral exponents of a variable. A polynomial in one variable ( say x ) contains only such terms as can be expressed in the form axⁿ, where ‘a’ is a constant and ‘n’ is a non-negative integer. In other words, a polynomial in x cannot have terms, such as 1/x, 1/x², 1/x and 1/x⁴ because they are not of the form xⁿ, where ‘n’ is a non-negative integer.

Example.1)  - 5x⁴ - 7 x + 3 is a polynomial in ‘x’ with three terms - 5x⁴,  - 7x, and here the term 3 is called a constant term.


Example.2)  - x² + -------- + 7 is not a polynomial because the



term -------- is not a form of axⁿ, where ‘n’ is a non-negative integer.


Polynomial in two or more Variable

A polynomial in two or more variables is a sum of terms that contain only non-negative integral exponents of those variables. For example, a polynomial in x, y & z is a sum of one or more terms of the form n xᵐ yᵖ zᵏ, where ‘n’ is any constant and m, p, & k are non-negative integers.

Examples.1) 10y²z + 8 x²y + 3 xz² is a polynomial in three variables x, y, & z.

Example.2) 21a⁴bcd⁴ + 8 ab²c²d - 10 abc⁵d is a polynomial in four variables a, b, c, and d.