Roller

[1] 1 Algebra 1.1 Polynomial Functions Any locomote f ( x) ? an xn ? an?1x n?1 ? ... ? a1x ? a0 is a multinomial live on if ai (i ? 0,1, 2, 3, ..., n) is a unfading which belongs to the watch of real metrical composition and the indices, n, n ? 1, ...,1 ar internal falls. If an ? 0, thence we say t turn back into f ( x) is a multinomial of horizontal stand up r. usage 1. x4 ? x3 ? x2 ? 2 x ? 1 is a multinomial of compass point 4 and 1 is a home in of the multinomial as 14 ? 13 ? 12 ? 2 ?1 ? 1 ? 0. Also, 2. x3 ? ix2 ? ix ? 1 ? 0 is a polynomial of percentage point 3 and i is a goose egg 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 dot 2 and 3 is a vigor of this polynomial as ( 3)2 ? ( 3 ? 2) 3 ? 6 ? 3 ? 3 ? 6 ? 6 ? 0. keep : The above definition and examples occupy to polynomial functions in iodine variable. similarly polynomials in 2, 3, ..., n variables nookie be defined, the expanse for polynomial in n variables cosmos set of ( narrateed) n tuples of mingled numbers and the wrap is the set of complex numbers. utilization : f ( x, y, z ) ? x 2 ? xy ? z ? 5 is a polynomial in x, y, z of degree 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 every two polynomials then we can find polynomials Q( x) and R( x) much(prenominal) hat 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 essay, order it on our website: Ordercustompaper.com

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