§ 2. Òåîðèÿ äåëèìîñòè ìíîãî÷ëåíîâ

                  ¹ 15. Èçâåñòíû äåëèìîå f(x), íåïîëíîå ÷àñòíîå q(x)
è îñòàòîê r(x). Íàéäèòå äåëèòåëü g(x).
15.01.
f(x) = x4 + 2x3 – x2 + 3x + 2,
q(x) = õ + 3,
r(x) = –6õ – 7;
15.02.
f(x) = x4 + x3 – 2x2 + 2x + 5,
q(x) = õ – 1,
r(x) = –2õ2 + 2õ + 7;
15.03.
f(x) = 4x4 + 2x3 – 2x2 + 2,
q(x) = 4õ2 + 10õ + 18,
r(x) = –2õ2 + 2õ + 7;
15.04.
f(x) = 6x6 + x5 – 2x4+2x3+3x2+3,
q(x) = 3õ2 – 4õ + 2,
r(x) = 7õ3 – 11õ2 + 10x – 1;
15.05.
f(x) = x4 + 3õ3 – 3õ2 + 3,
q(x) = x3 – x2 + õ + 1,
r(x) = õ – 1;
15.06.
f(x) = 9x4 – 3x3 – 30x2 + 8x – 26,
q(x) = –3õ2 + õ – 2,
r(x) = 12õ2 + 10;
15.07.
f(x) =  3x7 + 7x6 – x5 + x4 – 4x3 – x2 – 5x + 3, q(x) = x4 + 2x3 – õ2 + x – 1,
r(x) = õ2 – 4x + 2;
 15.08.
f(x) = x11 + x6 – 2x5–x4–3x3–1,
q(x) = õ6 – õ4 + x2 – 3,
r(x) = –õ2 + 2;
15.09.
f(x) = 6x14 – 3x3 + 2x2 – 2x + 4,
q(x) = 2x + 3,
r(x) = 20õ2 + 7;
15.10.
f(x) = x8 – 4x7 + 7x5–8x4–x3+14x2+x–2,  q(x) = x3 – 4x2 + 5,
r(x) = x + 3;
15.11.
f(x)=15x13+9x11 + 45x10+35x9+27x8+21x7+3x5–9x4+8x2–22x–13,
q(x) = 3x4 + 9x + 7,
r(x) = –õ2 – 2x + 8;
15.12.
f(x) = x5 + 2x4–3x3+2x2+x+1,
q(x) = õ + 1,
r(x) = –5õ3 + 5õ2 + 4õ;
15.13.
f(x) =3x5+4x4+x3–2x2 + x + 1,
q(x) = 3õ + 10,
r(x) = 12õ3 – 35õ2 + 31;
15.14.
f(x) = x4 + 2õ3 + õ + 2,
q(x) = 2x2 + 2x + 2,
r(x) = 2õ + 4;
15.15.
f(x) = x4 + 3x3 + 2x2 + 2x + 3,
q(x) = õ3 + 2x + 2,
r(x) = –2õ – 3;
 
15.16.
f(x) = 2x4 + 4x3 + 5x2 – x,
q(x) = õ2 + x + 1,
r(x) = –2õ – 1;
15.17.
f(x) = 2x4 + x3 + 2x2 + 7x + 6,
q(x) = õ2 – 2x + 1,
r(x) = –8õ – 4;
 
15.18.
f(x) = 4x4 + 3x3 + 2x2 + x + 1,
q(x) = 4õ2 – x – 1,
r(x) = 3õ + 2;
15.19
f(x) = 6x5 + 3õ4 + õ2 + 2,
q(x) = 6x + 3,
r(x) = –5õ2 – 15õ – 4;
15.20.
f(x) = x5 + 3x4 – 3x,
q(x) = õ2 + 3x + 1,
r(x) = –õ3 + õ2 + 1;
15. 21.
f(x) = x5 + 7x4 + 12x3–x2–2x–4,
q(x) = õ2 – 2õ + 25,
r(x) = –138õ2 + 75õ – 29;
15.22.
f(x) = 2õ6 – x5 –4x4+2x3+x2–4x +5,
q(x) = 2õ3 – 5õ2 + 8õ – 17,
r(x) = 38õ2 – 13õ + 4;
15.23.
f(x) = x4 + 2x3 – 4x2 + 17x – 15,
q(x) = õ2 + 3x – 5,
r(x) = 5;
15. 24.
f(x) = x5 + 2x4 – x3+5x2–x+6,
q(x) = õ2 + 5õ + 12,
r(x) = 5õ2 – 5õ + 1;
15. 25.
f(x) = 2x5 – 4x4 + x3+6x2+3x–5,
q(x) = 5õ – 14,
r(x) = 123õ3 – 16õ2 + 29õ + 9;
15.26.
f(x) = 4x3 – 2õ2 – õ + 1,
q(x) = 2x – 2,
r(x) = 3õ – 1;
15.27.
f(x) = 6x4 – 3x3 + 2x2 + 2x – 4,
q(x) = 2x + 3,
r(x) = 20õ2 – 7;
15. 28.
f(x) = 4x5 – 2x4 + 2x3 + 5x2 – 3x + 8,
q(x) = 2õ2 – 4õ + 8,
r(x) = –29õ2 + 17õ – 16;
15.29
f(x) = x3 + 6õ2 + 13õ + 2,
q(x) = x + 5,
r(x) = 8õ – 3;
15.30.
f(x) = x3 + 12õ2 + 35õ + 7,
q(x) = x + 7,
r(x) = õ2 + 7õ + 7;
15.31.
f(x) = 21x4–23x3+11x2+12x–16,
q(x) = 3x – 2,
r(x) = 5õ2 – 8;
15.32.
f(x) = 2x7 + 5x6 – 4x5 + 3x4 – x3 + 2x2 – 5x + 4, 
q(x) = 2x4 + õ3 – 4x2 + 8õ – 23,
r(x) = 5x2 – 8;
 
15. 33.
f(x) = x5 + 5x4+8x3+13x2+7x+16,
q(x) = õ3 + 3õ2 – õ + 5,
r(x) = õ2 + 1;
15. 34.
f(x) = x5 + 5x4 + 5x3 – 9x2 – 20x,
q(x) = õ2 + 3õ – 1,
r(x) = õ – 7;
 
15. 35.
f(x) = 12x4 –7x3–5x2–37x–11,
q(x) = 3õ – 4,
r(x) = –23õ2 – 7;
15. 36.
f(x) = x6 – x5 + 3x4 – 8x3 + 8x2 – 5õ + 3,
q(x) = õ3 + 2õ – 6,
r(x) = õ + 3.

 

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