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Please study

Polynomial before Adding Polynomials

if you have not already done so.

There we studied Definition, General form
and Degree of Polynomial. Also we provided
Link for study of Zeros, Simplified form
and arranging of Polynomials.

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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.

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.

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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