Page 47 - SM inner class 8.cdr

For example: 1. Addition of Algebraic Expression
3x + 5 is polynomial of degree 1. To add several positive like terms, we proceed
2
5x - 6x + 2 is a polynomial of degree 2. as follows :
3
2
And 4x - 2x + 7x + 8 is a polynomial of Step 1: Obtain all like terms.
degree 3.
Step 2: Find the sum of the numerical
coefficients of all terms.
Types of Polynomial
Step 3: Write the required sum as a like
Monomial: A polynomial with only one term
term whose numerical coefficient
is called a monomial.
is obtained in Step 2 and literal
3
-
For example 3 8x, x 2 4 6y . factor is same as the literal factors
,
Binomial: A polynomial with two terms is of the given like terms.
called a binomial. Two ways to solve addition of algebraic
2
For example 4x - 9 3x + 2y, -8xy + 3 expressions:
,
Trinomial: A polynomial with three terms is 1. Horizontal Method: In this method, all
called a trinomial. expressions are written in a horizontal
2
2
For example 2x - 3x + 3x y + 6xy + y line and then all the terms are arranged
7,
to the groups of like terms and then
Standard Form of a Polynomial added.
If the terms of a polynomial are either 2. Column Method: In this method each
arranged in ascending or descending order of expression is written in a separate row
their powers, then the polynomial is said to be such that there like terms are arranged
in its standard form. one below the other in a column. Then the
addition of terms is done column wise.
For example:
Example 1. Simplify (2x + 5y ) + (3x - 2y )
3
2
3
2
5 2 + 8x - 3x or 4x + 2x + 3x - 30
x
-
Solution:
Addition and Subtraction of Algebraic
By Horizontal Method:
Expression
(2x + 5y ) + (3x - 2y )
Let’s take an example–
= 2x + 5y + 3x - 2y
On a table we have 4 pencils and 2 books. We like terms are arranged together
cannot add the 4 pencils to the 2 books - they = 2x + 3x + 5y - 2y
are not the same kind of object. = 5x + 3y
If we get another 3 pencils and 6 books. So,
altogether we now have 7 pencils and 8 books. By Column Method:
We can’t combine any further quantities, since Put each variable in its own column; in this
they are different types of objects. case, the first column will be the x-column, and

Next, your sister comes in and grabs 5 pencils. the second column will be the y-column:
You are left with 2 pencils and you still have 2x + 5y
the 8 books. 3x - 2y

Similarly with algebra, we can only add (or 5x + 3y
subtract) similar “objects”, or those with the So the sum is : 5x + 3y.
same letter raised to the same power.

47
Mathematics In Focus - 8