19-12-2012, 06:34 PM
Polynomials
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Introduction
An algebraic expression in which variables involved have only non-negative integral powers is called a polynomial.
E.g.- (a) 2x3–4x2+6x–3 is a polynomial in one variable x.
(b) 8p7+4p2+11p3-9p is a polynomial in one variable p.
© 4+7x4/5+9x5 is an expression but not a polynomial
since it contains a term x4/5, where 4/5 is not
a non-negative integer.
Polynomials in one variable
A polynomial is a monomial or a sum of monomials.
Each monomial in a polynomial is a term of the polynomial.
The number factor of a term is called the coefficient.
The coefficient of the first term in a polynomial is the lead coefficient.
A polynomial with two terms is called a binomial.
A polynomial with three term is called a trinomial.
Points to Remember
A real number ‘a’ is a zero of a polynomial p(x) if p(a)=0. In this case, a is also called a root of the equation p(x)=0.
Every linear polynomial in one variable has a unique zero, a non-zero constant polynomial has no zero, and every real number is a zero of the zero polynomial.