Adding of Polynomials


 Title:-  Adding of Polynomials



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Today  I will explain the topic Adding of Polynomials which is a very important topic of mathematics for school going children.

  Table of Contents


To start my topic Let us first know 

 What is Polynomial?

Answer:-In Mathematics, a polynomial is an expression which consists one or more terms and coefficients that take part only the operations of addition, subtraction, multiplication, and positive integer power of variables and integer power will never be a negative one or a fraction,or never be the square root of variables .e.g, x² - x - 6  is a quadratic polynomial of variable x as the degree of the polynomial is 2 (in terms of degree if we consider) again it can be called as trinomial (if we consider its total terms).


How Polynomials are classified?

Answer:- Depending on terms polynomials are characterised in four types
and they are :-
(i) Monomial
(ii) Binomial
(iii) Trinomial
Again depending on degree polynomials are further divided in four types and they are:-
(i) Zero degree polynomial.
(ii) Linear or one degree polynomial.
(iii) Quadratic or two degree polynomial.
(iv) Cubic or three degree polynomial.
Now I will discuss on our main topic  Adding of Polynomials. To start this let us quick remember,

What are coefficient, literal factors, like terms and unlike terms?

Answer:- In simple words we can say that the numbers which are just before the terms in any algebraic expression are called; 2x + y +3 is a trinomial and the coefficients of x and y terms are 2 and 1 respectively.
  The terms other than coefficients are known as literal factors. In other words we can say that except coefficients all variables present in a term are called literal factors. e.g; 3xyz ,this is a monomial and literal factors if this term is xyz.
   The terms which have same literal factors may have different coefficients are known as like terms. e.g; 5xy²z , -7xy²z are like terms.
    The terms which have different literal factors are known as unlike terms. e.g; 6pqr, 6qrp² are unlike terms.

Find coefficients, literal factors, like terms and unlike terms.

Adding of Polynomials

Answer:- From the picture,

Coefficients :- 3,-2,5,1
                Literal factors:-xyz,xyp,mnl
                Like terms:- 3xyz,-2xyz
              Unlike terms:- xyp,mnl

Add the following polynomials.


3xyz , - xyz
   Answer:-        3xyz
                        - xyz


              (i) Polynomials are written vertically one after another.
           (ii) Both like polynomials and coefficients of upper and lower are 3 and -1 respectively. So simply subtracting 3 - 1 = 2 [ ∵ Here grater number is + 3, so after subtraction the results sign will be +, here it is +2]


Adding of Polynomials

     Answer:- 1st Method:-
                     - 2xyz
                    + 5 xyz

Rule (2) :-

        (i) First all terms are placed one after another vertically.
       (ii) Then,coefficients are simplified then the result  has come.
           2nd Method:-
              ∵ 3xyz + (- 2yxz) + 5zyx
    = 3xyz  - 2xyz + 5xyz
    = 8xyz - 2xyz
   = 6 xyz


    (i) Rearranging all terms and then they are written horizontally  one by one.
   (ii) Positive terms are added and then negative term is subtracted to get the result.


   -  x² + 2xy - 3z, 5x² -3xy +z, 4xy - z + 2x²
        1st Method:-
                       -  x² + 2xy - 3z
                         5x² - 3xy +  z
                         2x² + 4xy - z
                         6x²  + 3xy -3z


          (i) All like terms are put one after another vertically.
         (ii) Coefficients of the terms are simplified and then result comes.
2nd Method:-
 ∵ -  x² + 2xy - 3z + 5x² -3xy +z + 4xy - z + 2x²
= - x² + 5x² + 2x² + 2xy - 3xy + 4xy - 3z + z - z
= 6x² + 3xy - 3z


    (i) All like terms are put together horizontally.
   (ii) Coefficients of like terms are simplified and then result comes.


 x - 3y + 6z, p + y +5x, z +q  + r
      1st Method:-
                   x - 3y + 6z
                 5x + y            + p
                              + z            + q + r
               6x  - 2y  + 7z + p   + q + r


           (i) All like terms are put one under another vertically and unlike terms are written separately
        (ii) Coefficients of like terms are simplified and unlike terms are written as useul and then result comes.

         2nd Method:-
   x - 3y + 6z + p + y + 5x+ z +q  + r
 = x + 5x - 3y + y + 6z + z + p + q + r
 =  6x - 2y + 7z + p + q + r


          (i) All like terms are put one under another together and unlike terms are written separately.
         (ii) Coefficients of like terms are simplified and unlike terms are written as usual and then result comes.




      Adding of Polynomials can be done in two methods, and they are :- (i) Horizontal Method (ii) Vertical Method.

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What are the two methods of adding polynomials?

Answer:- The two methods of adding polynomials are :- (i) Vertical Method (ii) Horizontal Method.

What are the rules in adding polynomials?

Answer:- Rule(i) Polynomials are rearranged in order of highest degree to gradually lower degree. Rule(ii) Like terms are placed one after anothe vertically or placed one by one horizontally. Rule(iii) Like terms are simplified.

How to Add Polynomials Vertically?

Answer:- In vertical method,all the like terms are put one under another vertically and then simplifying them also keeping separate unlike terms.

What is called 1 term polynomial?

Answer:- An 1 term polynomial is called monomial.

How to Solve Adding Polynomials?

Answer:- All like terms are arranged one under another in case of vertical method and put together all like terms in case of horizontal method, then simplify the coefficients of them to get the result.

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