ADDING POLYNOMIALS - ADDITION, SUBTRACTION, EXAMPLES. LINKS FOR FURTHER STUDY

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Adding Polynomials :

While adding, similar terms are grouped together and each set of similar terms is simplified to a single term.

Example 1 of Adding Polynomials :

Add 5x2 + 3x - 7 and 2x2 - 4x + 9

Solution to Example 1 of Adding Polynomials:
The sum of the given Expressions = (5x2 + 3x - 7) + (2x2 - 4x + 9)
Grouping similar terms, we get
sum = (5x2 + 2x2) + (3x - 4x ) + (-7 + 9)
= (5 + 2)x2 + (3 - 4)x + (2)
= 7x2 - x + 2 Ans.
The above method of adding is called horizontal method.

We can also follow another method called column method in whichaddition can be done quickly, accurately and easily.

Step 1: First write the Expressions in descending order, if they are not already there in that order.Here the given polynomials are already in descending order.

Step 2: Now write down one expression below the other in order and then add.
5x2 + 3x - 7
2x2 - 4x + 9
------------------
7x2 - x + 2 Ans.
------------------

Example 2 of Adding Polynomials :

Add the following Expressions by column method.
5x3 - 3x + 4 and -9x3 + 12x2 -3

Solution to Example 2 of Adding Polynomials :
Step 1: First write the Expressions in descending order.If any term is missing write the coefficient 0 for it.Here first Expression does not have x2 term. So take it as 0.x2. Similarly second Polynomial does not have x term. So take it as 0.x.

Step 2: Now write down one Expression below the other in order and then add.
5x3 + 0.x2 - 3x + 4
-9x3 + 12x2 + 0.x - 3
-----------------------------
-4x3 + 12x2 - 3x + 1. Ans.
-----------------------------

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Subtraction : Adding Polynomials

Subtraction is similar to addition, except that the signs of the termsof the Expression to be subtracted are to be changed.

Example 3 of Adding Polynomials :

Take the two Expressions in Example 1 and subtract the second from the first by (i) horizontal method and (ii) column method.

Solution:
Let The two Expressions be denoted by A and B.
Then A = 5x2 + 3x - 7 and B = 2x2 - 4x + 9.
A - B = (5x2 + 3x - 7) - (2x2 - 4x + 9)
= (5x2 + 3x - 7) - 2x2 + 4x - 9
= (5x2 - 2x2) + (3x + 4x) + (-7 -9)
= 3x2 + 7x -16. Ans.
In column method, we follow the same procedure as in addition aboveexcept that the signs of the terms of the expression to be subtracted(written at the bottom) are changed.
  5x2 + 3x - 7
  2x2 - 4x + 9
(-)    (+)    (-)
-----------------
3x2 + 7x - 16 Ans.
-----------------

Example 4 Adding Polynomials :

Take the two Expressions in Example 2 and subtract
the second from the first by column method.

Solution:
We have to write the second Polynomial below the first
after arranging in descending order and puttiing 0 as
coefficient for the missing terms as done in case of addition.

Then we have to change the signs of the terms
of the bottom Polynomial and then add.

   5x3 + 0.x2 - 3x + 4
  -9x3 + 12x2 + 0.x - 3
(+)     (-)      (-)     (+)
---------------------------------
14x3 - 12x2 - 3x + 7. Ans.
----------------------------------

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