Содержание

 

 

 

 

 

§ 2. Теория делимости многочленов

№ 24. Найдите наибольший общий делитель многочленов f(x)  и g(x).

24.01.

f(x) = (х – 1)2×(х – 2)2 × (х + i),
g(x) = х5 – 2х3 + 4х2 – 3х + 2

24.02.

f(x) = х6 – 1,
g(x) = х14 – х + 1;

24.03.

f(x) = (х4 – 1) × (х + 2)2,
g(x)=х6–х54+2х3–3х2+3х–3;

24.04.

f(x)=(х3–3)22+2)(х+1)2,
g(x)=х6+5х5+7х4–15х2–21х–9;

24.05.

f(x)=(х–2)2(х–1)22+1),
g(x) = х3 – х2 – х + 1;

24.06.

f(x)=(х2+3)22–2)(х+2)2,
g(x) = х6 + 2х5 + 4х3 + 6х2 + 3;

24.07.

f(x)=(х–1)22+1)(х+ 1)2,
g(x) = х3 – х2 – х + 1;

24.08.

f(x)=(х2+2)23–2)(х + 1),
g(x)=х54+4х3+4х2+4х+4;

24.09.

f(x)=(х2–2)2(х–1)22+1),
g(x)=х5–5х4+11х3–19х2+2х–1;

24.10.

f(x)=(х–3)22+2)(х–1)2,
g(x)=х5–5х4+9х3–13х2+14х–6;

24.11.

f(x)=(х–2)2(х–1),
g(x)=х5–7х4+12х3+16х2–64х+48;

24.12.

f(x)=(х–1)42+х+1)2(х + 1),
g(x)=х5–2х43–х2+2х–1;

24.13.

f(x) = (х + 1)2 × (х + 3),
g(x) = х4 + х3 – 3х2 – 5х – 2;

24.14.

f(x)=(х–2)2(х+3)2(х+1)(х–1),
g(x)=х5+3х4+13х2+8х+24;

24.15.

f(x)=(х–2)3(х–1)22+1)2,
g(x)=5х4+11х3–19х2+24х–12;

24.16.

f(x)=(х+1)3(х–1)32+1),
g(x)=х5–3х4+7х3–13х2+12х–4;

24.17.

f(x)=(х+2)2(х–3)2(х2+1),
g(x)=х5–х4–9х3+5х2+16х–12;

24.18.

f(x)=(х–1)3(х + 2)2(х2 + 1),
g(x) = х4 – 2х3 + 2х2 – 2х + 1;

24.19.

f(x)=(х–4)2(х+2)2(х+3),
g(x)=х5–4х4–11х3+26х2+64х+32;

24.20.

f(x)=(х+4)3(х–2)22 – 3),
g(x)=х4+8х3+13х2–24х–48;

24.21.

f(x)=(х–2)3(х–1)3(х+1),
g(x) = х4 + 3х2 – 4х3 + 4х – 4;

24.22.

f(x)=(х–2)2(х + 3)2(х – 1),
g(x) = х4 – 6х3 + 13х2 – 12х + 4;

24.23.

f(x)=(х–3)2(х–4)22 + 2),
g(x)=х5–9х4+11х3+117х2

24.24.

f(x)=(х3–2)22+2)(х+1)2,
g(x)=х5+2х43–2х2–4х–2;

24.25.

f(x)=(х3–2)22 + 1)(х + 1)2,
g(x) = х9 – 3х3 – 2;

24.26.

f(x)=(х–1)52+1)242+1)3,
g(x)=х6+2х5–х4–4х3–х2+2х+1;

24.27.

f(x) = (х2 + 4) × (х + 3) × (х – 1)2,
g(x)=х5–х4+3х3–3х2–4х+4;

24.28.

f(x)=(х+1)2(х–2)2+11),
g(x)=х4+2х3+12х2+22х+11;

24.29.

f(x)=(х+1)3(х–2)2(х+3)2,
g(x)=х4+3х3–12х2–20х+48;

24.30.

f(x)=(х+4)2(х–2)3(х+1)2,
g(x) = х3 – 12х + 16;

24.31.

f(x) = (х2 + 3)3 × (х + 2)3 ×2 – 2)2,
g(x) = х6 + 5 + 4х3 + 6х2 + 3;

24.32.

f(x)=(х+3)2(х+2)(х – 1)4,
g(x) = х4 – 2х3 + 2х2 – 2х + 1;

24.33.

f(x)=(х+1)3(х–1)22+1)2,
g(x) = х3 – х2 – х + 1;

24.34.

f(x) = (х + 2) ×4 – 1) × (х – 3),
g(x)=х6–х54–2х3–3х2+3х–3;

24.35.

f(x) = (х2 + 1)2 × (х + 1)2 × (х – 1)3,
g(x)=х5–3х4+7х3–13х2+12х–4;

 

 

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