Question

What is the meaning of polynpmial

Answer 1

Hi dear

Your ans is here

⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐




IN MATHS

An expression of more than two algebraic term


Or

COMMONLY

Consisting of many terms

❤❤❤❤❤❤❤❤❤❤❤❤❤

Hope it will definitely help u


⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐

Answer 2

Hey There!!!!


Here I will let you know many things about a  Polynomial.



We will see everything from the meaning of the term, definition and all examples, along with its different types.


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Etymology 



Let's see where the word Polynomial  comes from.



Polynomial is made up of two parts:



Greek Root word Poly - meaning  many


Latin Root word Nomen - meaning name



It was derived from the word Binomial, by replacing bi  with poly


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Meaning



A Polynomial is an algebraic expression consisting of a single variable, where all terms have integral powers of the variable. 


For example, $x^2+3x+4$ is a polynomial. 


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The Naming of a Polynomial



A Polynomial can be named with single capital letters, with the variable name in round brackets. 


For example, a Polynomial in variable x can be named as P(x), Q(x), R(x), etc.


Similarly, a Polynomial in variable y can be named as P(y), Q(y), R(y), etc.



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Mathematical Definition




The most general form of a Polynomial is: 



$\boxed{P(x)=a_nx^n+a_{n-1}x^{n-1}+a_{n-2}x^{n-2}+...+a_1x^1+a_0}\\ \\ where \, a_n \neq 0 \, and \, n,n-1,n-2, ... \textrm{are whole numbers, and } a_n,a_{n-1},...,a_0\textrm{ are Real Numbers}$



A Degree of a Polynomial is the highest power of the variable. 



In The General Form, the highest power is n, so it is called an $n^{th}$ degree polynomial. 


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Some Points




-> For a polynomial to be an $n^{th}$ degree polynomial, the coefficient of $x^n$ cannot be Zero, i.e. $a_n\neq 0$


-> In all terms, the powers of the variable (say x) must be an Integer. 


-> All coefficients must be Real Numbers 

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Examples



-> $P(x) = -3x^3+2x^2+\frac{4}{5}x+9$ 


This is a Polynomial in variable x, Degree 3


-> $Q(y) = 7y^4-3y$


This is a Polynomial in variable y, Degree 4. [As you can see, coefficients of other terms can be zero. Only highest power co-efficient must not be zero.] 


-> $P(x) = x^{\frac{3}{5}}+x+3$


This is Not a polynomial. Here, the power of x in one term is not an integer.


-> $R(x)=4$


This IS a polynomial. It is a Zero Degree Polynomial. 


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Types of Polynomials




Some Polynomials are given special names: 



1) Linear Polynomial -> A polynomial of degree 1

E.g. $P(x)=3x+1$



2) Quadratic Polynomial -> A polynomial of degree 2

E.g. $Q(z) = -6z^2+3z+7$



3) Cubic Polynomial -> A polynomial of degree 3


E.g. $R(m) = m^3+3m$



4) Quartic Polynomial -> A polynomial of degree 4

E.g. $P(x) = 9x^4+7x^3+5x^2+3x+1$


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Hope it helps
Purva
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