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Describe polynomials .

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Answer 1

POLYNOMIALS

It's really a wide and nice concept of mathematics to understand.

Let's begin from basics :-

TERMS

Terms are nothing but a part of Algebraic Expressions which are formed by combination of variables and constants by using multiplication or division operator.

For Example :- 2p ( 2 = constant & p = variable)

But if two or more such terms are connected by addition or substraction then they are treated as a number of connected terms.

E.g. 2p + 3/b

It is having two terms 2p and 3/b separated by '+'.

Now let us have a brief look on constants and variables :-

Variables are nothing but English alphabet or symbol whose value varies from expression to expression.

e.g. a,b,c,d,p,q,r,x,y,z, ¶,¥ etc.

Constants are real numbers whose value remain fixed everywhere universally.

e.g. 1,2,...100,200....,57995,10^100 etc.

Algebraic Expression, It is a mathematical expression formed by algebra (constants and variable or any one of them).

e.g. 5, x , 35z, 568x + 56y , 6/7x - 56y + 2

Types of Algebraic Expressions

Based on the degree(highest power) of variable we can classify it as :

1. Linear having maximum power 1 of variable.

e.g. 2x + 4

2. Quadratic having maximum power 2 of variable.

e.g. 5x^2 + 3x + 5

3. Cubic having maximum power of 3 of variable.

e.g. 6y^3 + 5x + 7

4. Biquadratic having degree of 4 in varible.

e.g. 7z^4 - 6z^2 + 6z

and so on.

Now on the number of variables we can classify them as :-

1. Monomial (Having one term)

e.g. 5x^2

2. Binomial (Having two terms)

e.g. 56x + 6y

3. Trinomial (Having three terms)

e.g. 90x + x^2 - 3

and so on.

All these can be called as polynomial.

Now let's understand Polynomial :

A Polynomial is an Mathematical Expression having more than two terms following a proper format I.e.

a0xn + a1x^(n−1)+ a2x^(n−2) + a3x^(n−3) + ..... + an

where a0, a1, a2, a3, ....., an are given numbers 'n' is a non-negative integer and x is a variable.

◆Polynomial is a special algebraic expression.

Answer 2

Answer:

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In mathematics, a polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables. An example of a polynomial of a single indeterminate x is :

${x}^{2} + 4x + 7$

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Types of polynomial:

The three types of polynomials are:

• Monomial.

• Binomial.

• Trinomial.

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polynomial in one variable:-

Polynomials in one variable are algebraic expressions that consist of terms in the form axn a x n where n is a non-negative (i.e. positive or zero) integer and a is a real number and is called the coefficient of the term. The degree of a polynomial in one variable is the largest exponent in the polynomial.

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Polynomial in two variable:-

Polynomials in two variables are algebraic expressions consisting of terms in the form axnym a x n y m . The degree of each term in a polynomial in two variables is the sum of the exponents in each term and the degree of the polynomial is the largest such sum

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Extra related to this:-

degree of the polynomial:-

the degree of a polynomial, denoted, is the highest of the degrees of the polynomial's monomials with non-zero coefficients. The degree of a term is the sum of the exponents of the variables that appear in it, and thus is a non-negative integer.

The following names are assigned to polynomials according to their degree:

Special case – zero (see § Degree of the zero polynomial below)

• Degree 0 – non-zero constant.
• Degree 1 – linear.
• Degree 2 – quadratic.
• Degree 3 – cubic.
• Degree 4 – quartic (or, if all terms have even degree, biquadratic)
• Degree 5 – quintic.

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