We now study a special type of function Consider 1. f ( x ) = 7x3 - 4x2 + 3x - 1 3. f ( y ) = 4y2 + Ö3y - 1 4. f ( y ) = y½ - 4y2 + y + 3 5. f ( z ) = z-2 + 5z + 1 ii) Indices of y and z in (4) and (5) are negative and fraction. First three expressions or functions are polynomials whereas forth and fifth are not polynomials. At this stage, we restrict our study of polynomials as a special type of function whose domain is a set of reals.
Definition: If Note :(I) (II) There are ( n + 1 ) terms in (1) (III) If For examples, p ( x ) = 5, p ( x ) = 3/2 etc. (IV) If all coefficients including a constant are zero. Then the polynomial is called ‘ zero ’ polynomial. A polynomial with only one term is a monomial.A polynomial with two terms is a binomial. A polynomial with three terms is a trinomial. (V) Usually polynomial is written in descending order of its powers of variable say x. ( standard form ). (VI) The degree of a polynomial is the exponent in the term with the highest power. For example, x5 + 7x3 - 3x + 2 has degree 5. 2x4 + 3x3 - 3 has degree 3. 3m2 + 4m - 1 has degree 2. x - 2 has degree 1 We do not define the degree of 0 i.e. zero polynomial. |
3.1 -
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are real
numbers and n is zero and positive integer then the function P is given
by 
is
called a " polynomial in x over reals " .
then (1) becomes 
which is a constant. Such polynomials are called constant polynomials.