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 heels 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 direct 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 multinomial of leg 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 decimal point 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 arse be defined, the domain for polynomi al in n variables human beings mark off 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 both two polynomials then we can find polynomials Q( x) and R( x) such wear P( x) ? ?( x) ? Q( x) ? R( x) where the degree ! of R( x) ? degree of Q( x). Q( x) is called the quotient 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 full-of-the-moon essay, order it on our website: BestEssayCheap.com

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