what is polynomial and give 3 example each for polynomial and non(not)polynomial
Answers
Answer:
We can perform arithmetic operations such as addition, subtraction, multiplication and also positive integer exponents for polynomial expressions but not division by variable.
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Degree of a Polynomial.
Polynomial Degree Example
Cubic Polynomial 3 6x3+4x3+3x+1
Quartic Polynomial 4 6x4+3x3+3x2+
Step-by-step explanation:
Polynomials
Polynomials are algebraic expressions that consist of variables and coefficients. Variables are also sometimes called indeterminates. We can perform arithmetic operations such as addition, subtraction, multiplication and also positive integer exponents for polynomial expressions but not division by variable. An example of a polynomial with one variable is x2+x-12. In this example, there are three terms: x2, x and -12.
Also, Check: What is Mathematics
The word polynomial is derived from the Greek words ‘poly’ means ‘many‘ and ‘nominal’ means ‘terms‘, so altogether it said “many terms”. A polynomial can have any number of terms but not infinite. Learn about degree, terms, types, properties, polynomial functions in this article.
Table of Contents:
Definition
Notation
Degree
Terms
Types
Monomial
Binomial
Trinomial
Properties
Equations
Function
Solving Polynomials
Linear Polynomial
Quadratic Polynomial
Operations
Addition
Subtraction
Multiplication
Division
Examples
FAQs
What is a Polynomial?
Polynomial is made up of two terms, namely Poly (meaning “many”) and Nominal (meaning “terms.”). A polynomial is defined as an expression which is composed of variables, constants and exponents, that are combined using the mathematical operations such as addition, subtraction, multiplication and division (No division operation by a variable). Based on the numbers of terms present in the expression, it is classified as monomial, binomial, and trinomial. Examples of constants, variables and exponents are as follows:
Constants. Example: 1, 2, 3, etc.
Variables. Example: g, h, x, y, etc.
Exponents: Example: 5 in x5 etc.
Notation
The polynomial function is denoted by P(x) where x represents the variable. For example,
P(x) = x2-5x+11
If the variable is denoted by a, then the function will be P(a)
Degree of a Polynomial
The degree of a polynomial is defined as the highest degree of a monomial within a polynomial. Thus, a polynomial equation having one variable which has the largest exponent is called a degree of the polynomial.
Polynomial Degree Example
Constant or Zero Polynomial 0 6
Linear Polynomial 1 3x+1
Quadratic Polynomial 2 4x2+1x+1
Cubic Polynomial 3 6x3+4x3+3x+1
Quartic Polynomial 4 6x4+3x3+3x2+2x+1
Example: Find the degree of the polynomial 6s4+ 3x2+ 5x +19
Solution:
The degree of the polynomial is 4.
Terms of a Polynomial
The terms of polynomials are the parts of the equation which are generally separated by “+” or “-” signs. So, each part of a polynomial in an equation is a term. For example, in a polynomial, say, 2x2 + 5 +4, the number of terms will be 3. The classification of a polynomial is done based on the number of terms in it.
Polynomial Terms Degree
P(x) = x3-2x2+3x+4 x3, -2x2, 3x and 4 3
Types of Polynomials
Polynomials are of 3 different types and are classified based on the number of terms in it. The three types of polynomials are:
Monomial
Binomial
Trinomial
These polynomials can be combined using addition, subtraction, multiplication, and division but is never division by a variable. A few examples of Non Polynomials are: 1/x+2, x-3
Monomial
A monomial is an expression which contains only one term. For an expression to be a monomial, the single term should be a non-zero term. A few examples of monomials are:
5x
3
6a4
-3xy
Binomial
A binomial is a polynomial expression which contains exactly two terms. A binomial can be considered as a sum or difference between two or more monomials. A few examples of binomials are:
– 5x+3,
6a4 + 17x
xy2+xy
Trinomial
A trinomial is an expression which is composed of exactly three terms. A few examples of trinomial expressions are:
– 8a4+2x+7
4x2 + 9x + 7
Monomial Binomial Trinomial
One Term Two terms Three terms
Example: x, 3y, 29, x/2 Example: x2+x, x3-2x, y+2 Example: x2+2x+20