§ 2. Теория делимости многочленов

                       № 16. Найдите НОД многочленов f(x) и g(x) с помощьюалгоритма
Евклида.
16.01.
f(x) = х6 – 2x3 – 4x2 – 8x – 3,
 
g(x) = 3х4 – 4х3 + 8х2 – 5х – 4;
16.02.
f(x) = х7 + 3х6 – 11x5 + 15x2 + 2x + 10,
 
g(x) = х6 + 5х5 – х4 – 3х3–10х2–х–5;
16.03.
f(x) = –12х5+28х4 –17x3–27x2+22x–4,
 
g(x) = – 6х2 + 5х – 1;
16.04.
f(x) =  14x6 – 24x5 + 38x4 + 15x3 – 123x2 + 56x + 10,
g(x) = 14x4 – 24x3 + 66х2 – 33х – 5;
16.05.
f(x) = 3х5 + 4х4 – 4x3 – 6x2 + x + 2,
g(x) = 3x4 + 7x3 – 7х – 3;
16.06.
f(x) = 2х5+21х4+51x3–41x2–47x+26,
g(x) = 2x4 + 23x3 + 72х2 + 20х – 31;
16.07.
f(x) = 3х5 + 3х4 – 3x3 – 6x – 3,
g(x) = 3x4 + 2x3 + х2 + 2х – 2;
16.08.
f(x) = 3х6 – 21х4 + 24x3 – 21x + 21,
g(x) = 3x5 – 7x3 + 3х2 – 7;
16.09.
f(x) = 3х5 + 5х4 +6x3+6x2+2х+1,
g(x) = x3 + х2 + х + 1;
16.10.
f(x) = –4х4 + х3 + x2 + 15x – 13,
g(x) = 2x4 – 7x + 5;
16.11.
f(x) = –10х4 – х3–10x2+14x+7,
g(x) = –2x4 – 2х2 + 3х + 1;
16.12.
f(x) = х4 + х3 – 3x2 + 2x – 1,
g(x) = x3 – 3x2 + 5х – 3;
16.13.
f(x)=4х5+2х4 +4x3+11x2–4х+3,
g(x) = 4x4 + 2х3 + 9х;
16.14.
f(x) = х5 + 2х4 – 4x3–x2+6х–4,
g(x) = x4 + 3х3 – х2 – 3х + 2;
16.15.
f(x) =  x5 – 4x4 – 31x3 + 125x2 – 100x + 384,
g(x) =
16.16.
f(x) = 3х5 + 4х4 – 4x3–6x2+х+2,
g(x) = 3x4 + 7х3 – 7х – 3;
16.17.
f(x) = 2х5 + x3 +2x2–6х–3,
g(x) = 2x4 – 2х3 – х2 + 3х – 3;
 
16.18.
f(x) =  2x6 + 2x5 + 2x4 + 7x3 + 2x2 + 4x + 5,
g(x) = 2х5 + 2x4 + 4x3 + 5х2 + 2;
 
16.19.
f(x) = х5 – 2х4 + x3 + х – 1,
g(x) = x4 – 2х3 + х2 – х + 1;
16.20.
f(x) = 2х5 – 4х4 –4x3–х2+х–1,
g(x) = x4 – 3х3 + х2 – х – 2;
16.21.
f(x) = х5 – 3х4 + 3x3–x2–2х+2,
g(x) = x4 + 2х3 – 3х2 – х + 1;
16.22.
f(x) = 4х5 + х4 –3x3+2x2–6х+5,
g(x) = 4x4 + х3 + 10х;
16.23.
f(x)=х5 – 7х4 +19x3–25x2+16х–4,
g(x) = x4 – 3х3 + 3х2 – х;
16.24.
f(x) = 3х5 + 2х4 +4x3–x2–4х+8,
g(x) = x4 – х3 + 2х2 – 2х – 4;
16.25
f(x) =  2x5 + 3x4 – 13x3 –10x2+21x+6,
g(x) = 2х4 + 5x3 – 8x2 – 19х + 2;
16.26.
f(x) =  x5 + 3x4+2x3+6x2,
g(x) = х4 + 2x3 – 3x2 + 4х;
16.27.
f(x) = 12x5 – 34x4 – 15x3 + 16x2 – 5x – 5,
g(x) = 12х4 – 22x3 + 19x2 + х + 7;
16.28.
f(x) =  x5 – 8x4 +2x3–5x2+3x–1,
g(x) = х4 – 2x3 + 4x2 – х + 2;
16.29.
f(x) =  x5 + 5x4 + 3x3 – 9x2,
g(x) = х4 + 3x3 + 3x2 + 9х;
16.30.
f(x) =  4x5–6x4+10x3–7x2+2x–3,
g(x) = 2х4 – 3x3 + 4x2 – 2х – 1;
16.31.
f(x) =  x5 + x4 – 3x3 + 9x2,
g(x) = х4 + 2x3 – 8;
16.32.
f(x) = 2х6 + 3x5 – 12x4 + 22x3 – 9x2 – 11x – 5,
g(x) = 2х4 + 5x3 – 11x2 – х + 5;
16.33.
f(x) = х6 – 7x5 + x4 – 2x3 – 35x2 + 5x – 35,
g(x) = х4 – 7x2 + х – 7;
16.34.
f(x) = х6 + 3x5 + 3x4 + 7x3 + 3x2 + 4x + 1,
g(x) = х4 + 3x3 + 2х2 + 4х + 1;
16.35.
f(x) = х6 – 4x5 + 14x4 – 38x3 + 49x2 – 75x + 25,
g(x) = х4 – 4x3 + 7х2 – 11х + 5;
16.36.
f(x) = –2х6 + 4x5 + 9x4 – 19x3 – 6x2 + 15x + 2,
g(x) = –2х4 + 4x3 + 5х2 – 9х – 2.

 

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