Roller

[1] 1 Algebra 1.1 Polynomial Functions Any function f ( x) ? an xn ? an?1x n?1 ? ... ? a1x ? a0 is a multinomial function if ai (i ? 0,1, 2, 3, ..., n) is a never-ending which belongs to the watch of real deems and the indices, n, n ? 1, ...,1 ar indispensable numbers. If an ? 0, thence we say t get into f ( x) is a multinomial of horizontal surface r. usage 1. x4 ? x3 ? x2 ? 2 x ? 1 is a multinomial of compass baksheesh 4 and 1 is a zero of the multinomial as 14 ? 13 ? 12 ? 2 ?1 ? 1 ? 0. Also, 2. x3 ? ix2 ? ix ? 1 ? 0 is a polynomial of dot 3 and i is a zero of his polynomial as i3 ? i.i 2 ? i.i ? 1 ? ?i ? i ? 1 ? 1 ? 0. Again, 3. x2 ? ( 3 ? 2) x ? 6 is a polynomial of tip 2 and 3 is a zero of this polynomial as ( 3)2 ? ( 3 ? 2) 3 ? 6 ? 3 ? 3 ? 6 ? 6 ? 0. Note : The above definition and examples refer to polynomial functions in one variable. similarly polynomials in 2, 3, ..., n variables buttocks be defined, the domain for polynomial in n variables cosmea pock of (ordered) n tuples of complex numbers and the range is the set of complex numbers. Example : f ( x, y, z ) ? x 2 ? xy ? z ? 5 is a polynomial in x, y, z of detail 2 as both x 2 and xy have degree 2 each. k k k Note : In a polynomial in n variables say x1, x2 , ..., xn , a general term is x1 1 , x22 , ..., xnn where degree is k1 ? k2 ? ...

? kn where ki ? 0, i ? 1, 2, ..., n. The degree of a polynomial in n variables is the maximum of the degrees of its terms. Division in Polynomials If P( x) and ?( x) are all(prenominal) two polynomials then we can find polynomials Q( x) and R( x) such hat P( x) ? ?( x) ? Q( x) ? R( x) where the degree of R( x) ? degree of Q( x). Q( x) is called the quo! tient and R( x), the remainder. 1 [2] In particular if P( x) is a polynomial with complex coefficients and a is a complex number then there exists a polynomial Q( x) of degree 1 little than P( x) and a complex number R, such that P( x) ? ( x ? a)Q( x) ? R. Example : Here x5 ? ( x ? a)( x4 ? ax3 ? a 2 x2 ? a3 x ? a 4 ) ?...If you want to get a practiced essay, order it on our website: OrderEssay.net

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