ARITHMETIC OF POLYNOMIAL

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 ALGEBRA - POLYNOMIALS



TYPES OF POLYNOMIALS

1) POLYNOMIALS BASED ON TERMS

MONOMIAL : The expression which contains only one term is called as monomial.  

Example: 5a, 3x

BINOMIAL : The expression which contains two terms is called as binomial.

Example: 5x+3, 3a+2b

TRINOMIAL : The expression which contains only three terms is called as trinomial.

Example: 4X2+2X+5

POLYNOMIAL : The expression which contains two or more that many terms are called as polynomials

2) POLYNOMIALS BASED ON DEGREE

CONSTANT : A polynomial of degree zero is called as constant polynomial. 

Example: 5, 7

LINEAR : A polynomial of degree one is called as linear polynomial.

Example: 4x, 7a

QUADRATIC : A polynomial of degree two is called as quadratic polynomial.

Example: 4X2+2X+5

CUBIC : A polynomial of degree three is called as cubic polynomial.

Example: 3x3- 4X2+2X+5

ARITHMETIC OF POLYNOMIAL

ADDITION OF POLYNOMIAL

The addition of two polynomials is called as addition of polynomials.

Example: P(x) = 4x2+2x3-3x+5  and q(x) = x2 + 2x + 4 then find p(x) + q(x)

p(x) + q(x) = 4x2+2x3-3x+5 + ( x2 + 2x + 4 )

                   =  2x3 + 4x2 + x2 -3x + 2x +5 + 4

                   = 2x3 + 5x2- x + 9 is the answer.

SUBTRACTION OF POLYNOMIAL

The subtraction of two polynomials is called as subtraction of polynomial.

Example: P(x) = 4x2+2x3-3x+5  and q(x) = x2 + 2x + 4 then find p(x) - q(x)

p(x) - q(x) = 4x2+2x3-3x+5 - ( x2 + 2x + 4 )

                  = 2x3+  4x2  - x2  -3x - 2x - 4 +5

                  = 2x3+ 3x2 - 5x + 1 is the answer.

MULTIPLICATION OF POLYNOMIAL

The multiplication of two polynomials is called as multiplication of polynomial.

Example: P(x) = 2x+5  and q(x) = x2 + 2x + 4 then find p(x) * q(x)

p(x) * q(x)   =  (2x+5)( x2 + 2x + 4)

                    = 2x3+4x2+8x+5x2+10x+20

                      =   2x3 +9x2+18x+20


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