Mathematics-Algebraic Equations / Polynomial Equations
In mathematics algebraic equation also called polynomial equations over a given field is an equation of the form P=Q, where P and Q are polynomials over that field.
X2 + X*Y - 5 = Y5 + XY3 - 4 is an algebraic equation over the field. Two equations are said to be equivalent if they have the same set of solutions. In general A = B if A - B = 0;
The polynomial is either Zero or can be written as one or more non-zero terms. The number of terms is finite. The terms consist of constants and variables . Constants are coefficient of a term and is multiplied by variables that is indeterminates of a term. Each variable may have an exponent that is non-negative integer[ natural number].
The exponent of a variable in a term is called degree of a variable and degree of a polynomial is largest degree of any variable in the term. Degree of term is sum of degrees of variable in the terms. A term without variable is called constant term. The degree of constant term is zero.
Example::
P = 8x2y, in this degree of x is 2 and degree of y is 1. So degree of total term is called 3 and 8 is the coefficient of a term. x and y are called variables of a term.
8x2 - 4y + 6 = 0; in this degree of a polynomial is 2 , because highest degree in this term is 2 that for the variable x. The sum , product, composition of a two polynomial is also another polynomial and derivative of a polynomial is also one polynomial. This is the elementary properties of a polynomial.
