POLYNOMIAL
An algebraic expression which consists of two or more terms is called a polynomial.
For example, a + b, x3 - y3 , x2 + x y + y2.
1) A polynomial which consists of exactly two terms is a binomial.
For example 2 x2 + x, x2 + y2.
2) A polynomial which consists of exactly three terms is a trinomial.
For example, x2 + 3 x + 2, a2 + a b + b2
etc. Usually a polynomial is
written either in the ascending or descending powers of the variable,
say x. This form of a polynomial
is called a standard form. For example x4
+ 3 x3 + x2
+ 7x + 5 and 2 + 3 y + 7 y2
- y3 are polynomials in the standard form. Descending
order is used more commonly.
Addition:
In order to add given polynomials, we adopt two steps.
1) Arrange the given polynomials, such that like terms are in one column.
2) Add the coefficients of each column separately.
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Subtraction :
This is done in two steps :
1) Arrange the given polynomials, such that like terms are in one column.
2) Change the signs of the terms of the polynomial and then add.
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Example Add 4 a - 3 b, - 2 a + b, 5 a - 3 b and - 6
a + 4 b
Solution: The required sum
=( 4 a - 3 b ) + ( - 2 a + b ) + ( 5 a - 3 b ) + (- 6 a + 4 b )
= ( 4 a - 2 a + 5 a - 6 a ) + ( - 3 b + b - 3 b + 4 b )
= ( 9 a - 8 a ) + ( 5 b - 6 b )
= a + ( - b )
= a - b
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