Nội dung text Lecture Notes R_F Theorem.pdf
Syllabus R/F Theorem Polynomials The division algorithm of polynomials -Many Terms Poly + Nomials But at least two terms an + b = 0 Linear Eg. Degree = 1 an + bu+ c = 0 Quadratic Eg. Degree = 2 ar+ bu + cu+ d = 0 Cubic Eg. Degree = 3 and + bu+ cu + du + e = 0 Quartic/Bi-Quadratic Degree =& ->Quotient - 5 Divisor = 3 5->Dividend 3 3 -> 2> Remainder Dividend = (Divisor) (Quotient) + Remainder Dividend = (D) (Q) + R 2 - > 2nd Factor 6 First 3 6 - Factor - 6 0Remainder
3 2x? -3u"-1 divided by n -4 2x2+5n+20 Quotient: x -42x3-34+ On - 4 3 = z za-Bu - t 5x2 - = Su 5x2 + On - 4 N 5x2-zon - + zox = 20 I 201 - 4 zon-80 - t 76 ((x) = 2n + 5n + 20 , R= 76 9 Su" + 13n-19 divided by 1-1 -6x3-6x -6x-19-> Quotient -x + 16x" + On + On + 13x-19 - Quotient 6x" = Ga Gut - --6x3 -x 6x3 + On + 13x-19 3 Ga ou" = Gu En = -6x2 - 6x2 6u2 = + 6n 13x-19 - 192-19 am = - 19 -x 192-19 - t 0 - >Remainder