LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

DEGREE OF A TERM

**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 x⁴yᶟz⁵ 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/xᶟ 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.**

** 5x **

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

**3**

**5x**

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

** 3 **

__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 abc⁵dᶟ is a polynomial in four variables a,
b, c, and d.**