Math, asked by harshkaur854, 1 year ago

explain me chapter polynomials of maths


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Answers

Answered by sumitlegendary
3
polynomials

to multiply a polynomial by a monomial we multiply each term of the polynomial by the monomial and add the product so obtained for example letters considered a monomial and a binomial se 2 x square and Bracket 3 X + 2 X + Y bracket

degree of a polynomial in one variable if the polynomial is 130 Abul then the highest exponent power of the value is called degree of polynomial example 2 X + 3 is a polynomial in X of degree one

let's know what is polynomial and algebraic expression in which the variables involved have only one negative integral powers is called a polynomial let's take a example 3 - 2 X + 7 x square + 3 X is a polynomial in one variable X only

second example 2 X square + 3 x y minus y square is a polynomial in two variables X and Y there are lot of more expressions

degree of a polynomial can be done by two or more variables in the case of polynomial in two or more than two variables the sum of the power of the variables in each term is taken up and the highest some so obtained is called the degree of polynomial let's take an example 5 x y minus 2 X is a polynomial in X and Y of degree 2

simplified form of a polynomial polynomial is said to be simplified if it contains all unlike terms

let's take a example the simplified form of 6x square + 2 X + 5 - 3 x is 3 X square + 2 X + 5

ascending order of a polynomial if we arrange the terms of a polynomial in increasing order of degrees then the polynomial is said to be in ascending order let's take us an example 5 + 3 X + 6 x square is in ascending order

descending order of a polynomial if we arrange the terms of a polynomial in decreasing order of degrees then the polynomial is said to be in descending order let's take an example 3 x to the power 4 + 5 x cube + x square + 11x minus 1 is in descending order


division of a polynomial by monomial to divide a polynomial by a monomial we divide each term of the polynomial by the monomial


division of a polynomial
arrange the two polynomials in decreasing order of their degrees the first polynomial is the divided and the second is the division the degree of the division is equal to or less than the degree of dividend

to get the first term of the quotient divide the first term of the divided by the first term of the divisior

now multiply the first term of the questioned by all terms of the division and write all the results below the divident

subtract the divided and the result obtained in the previous step to get a polynomial which becomes the next dividend

continue the process till we get the remainder 0 or a polynomial of a degree less than the degree of divisior

note that after dividing a polynomial if the reminder is zero we can say that the divide and is completely divisible or exactly divisible or simply divisible by the division.

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