Mathematics Algebras

DEGREE OF POLYNOMIAL                      The degree of a polynomial  is the largest of the degrees of the individual  terms.  Add the degrees of  the  variables of each term to decide  what is the degree of the polynomial.                   Degree of terms 1is 2 (1+1=2)                 Degree of terms 2 is 6 (2+4=6)                Degree of terms 3 is 7 (5+2=7)                    is the degree of the polynomial.                       

POLYNOMIAL EQUATION                A Polynomial equation  in two  variable  is an equation of the from                 P(x,y)= Q( x,y)            Where both P(x,y)and Q(x,y) are Polynomial is two variable.  EXAMPLE:                  *  xy+2 =y^2-3x-4                       (xy+2  is a quadriatic polynomial.  So is y^2-3x-4)                * y-x=2                (y-x is a linear Polynomial. 2 is a constant Polynomial)                *x^2-5x+y-2= -7xy-y+2              *3x^2-xy+4y^2-5x+6-7=0           Domain of Polynomial equation           ...

Numbers of terms                 Monomial :  A polynomial having one terms is called Monomial.                  Ex:  5, 6m ,13 ab            Binomial : A polynomial having two terms is called Binomial.                  Ex : 5x+3 , 4a -2 , 10p+1          Trinomial : A polynomial having three terms is called Trinomial.                  Ex: 5x^2+8x+8 , 3a^2+a+ 9   

Polynomial based on degree          Contant :  A polynomial  of degree zero is called Polynomial                 Ex: 5, -7, 2÷3 ,√5 Linear : A polynomial of degree one is called  Linear polynomial .               Ex: 5x +2, 6y-8 Quadriatic : A polynomial of degree two  is  called quadriatic polynomial                  EX: 2√5x^2+8x-4 Cubic: A polynomial of degree three is called  Cubic polynomial.              Ex : 12y^3 , 6m^3 -7m

TYPES OF BASIC POLYNOMIALS  EXPLANATION        1) MONOMIAL:  Monomial is a polynomial containing 1 term                 Ex: 3,4a       2) BINOMIAL  : Binomial is a polynomial  containing 2 terms                 Ex: (3+7x) ,(x-3)       3) TRINOMIAL: Trinomial is a polynomial containing 3 terms                  EX: (1+X+5X^2), (a+2b+c)      4) QUADRINOMIAL: Quadrinomial is a polynomial containing 4 terms                  EX:(a+2b+c+4) , (3x +3x^2y+3xy^2+4)          

POLYNOMIAL  TYPES                      POLYNOMIAL                Poly - many            Nomial- part(term) POLYNOMIAL- MANY TERMS  TYPE OF BASIC POLYNOMIAL           1) Monomial          2) Binomial            3) Trinomial           4) Quadrinomial

POLYNOMIAL       DEFINITION                              If power of a variable  are    Positive (+ve) integers than it is called Polynomial.                       It is denote by P    Eg:           5,4x+4y    

FOR EXAMPLE                   TO subtract 6y from 12.                 We can add 12 y and (-6y)                  Thus we have. 12y+ (-6y)= 12y-6y                                                             =y(12-6)                                                         =6y     Now, let us subtract  -mn from 3mn.  Additive  inverse of -mn  is mn . Hence  , we have to add mn with 3mn . Thus,                       3mn+mn=mn(3+1)             ...

ADDITION AND SUBTRACTION OF ALGEBRAIC EXPRESSIONS                       The part of algebra expression which are combined by the signs '+' or '-' are called terms of the expression.                    Subtraction of a term can be looked as addition of  its additive inverse as we saw in Subtraction of integers. To understand Subtraction of Algebraic expression, let us consider Subtraction of Algebraic expression with one terms.