§ 1. Ìíîãî÷ëåíû íàä îáëàñòüþ öåëîñòíîñòè

 ¹ 4. Ðàçäåëèòå ñ îñòàòêîì ìíîãî÷ëåí f(x) íà äâó÷ëåí

  g(x) = (õ – ñ), åñëè:

4.01.

à) f(x) = 3õ6 + 2x5 – x4 + 3x3 + x –3, g(x) = x – 1;
á) f(x) = iõ5 +(i – 1)x4 + ix3 + (1 + 2i)x +2, g(x) = x – 1 – i;

4.02.

à) f(x) = õ8 – 2x7 + x6 + 2x5 – 4x4 + 3x3 – x2 + 2x –1, g(x) = x – 2;
á) f(x) = õ6 – 3x5 +(3 + i)x4 + 3ix3 – 4ix2 +(4 + 3i)x + i, g(x) = x – 1 – i;

4.03.

à) f(x) = 2õ6 – 3x4 + 4x2 – 2x +1, g(x) = x + 2;
á) f(x) = õ6 –2ix5 + (1 –i)x4 + 2x3 + ix2 +1, g(x) = x – i;

4.04.

à) f(x) = 2õ8 – x6 – 3x4 – 2x +3, g(x) = x + 3;
á) f(x) = õ6 + ix5 – (1 + 2i)x4 + x2 – 1 – 3i, g(x) = x – 2 + i;

4.05.

à) f(x) = 3õ7 – x6 + 3x3 – 2x +5, g(x) = x + 1;
á) f(x)=õ6+(1–i)x5+2ix4+(3+3i)x3+x2+(2i–1)x–2+3i, g(x) = i –1;

4.06.

à) f(x) = 2õ5 – 5x3 – 3x2 +4, g(x) = x – 2;
á) f(x) = (1 – i)õ5– ix4+ix3 +(3 – 5i)x2 +(1 –2i)x – 4+3i, g(x) = x – 1 + i;

4.07.

à) f(x) = 4õ7 – 3x4 + 2x2 – 3x –3, g(x) = x + 2;
á) f(x) = iõ5+ (1 – i)x4 + (–2 + i)x3 + ix + 3 – i, g(x) = x – 1 + i;

4.08.

à) f(x) = 2õ5 + 4x4 – 5x3 + 3x22, g(x) = x + 2;
á) f(x) = (1 + i)õ5+ ix4 + (1 – 2i)x3 + (i –1)x2 – 9 + 8i, g(x) = x – 2 + i;

4.09.

à) f(x) = 3õ5 – 2x4 + x25, g(x) = x – 4;
á) f(x) = iõ5+ (i – 2)x4 + (1 + i)x3 + ix + 4 + i, g(x) = x – i;

4.10.

à) f(x) = 2õ7 + x5 – 3x3 + x – 4x, g(x) = x + 3;
á) f(x) = (3 + i)x6 – (2 – i)x4 + 3x3 – ix2 +3, g(x) = x + 1 – 2i;

4.11.

à) f(x) = 2õ5 + 5x4 – 2x3 + 2x2 + 5x +20, g(x) = x + 3;
á) f(x) = (2 + 3i)x5 – 2(4 + 5i)x4 – 15ix3 + (6 + 13i)x2 +  8(3 + 2i)x + 55 + 18i, g(x) = x – 3 + 2i;

4.12.

à) f(x) = 4õ5 – 5x3 + 2x2 – 8x, g(x) = x + 3;
á) f(x) = 3x5 – ix4 + (2 – 3i)x3   7x + 1 – 2i, g(x) = x – 1 + 2i;

4.13.

à) f(x) = 2õ5 + 2x3 + x2 – 4x +1, g(x) = x + 2;
á) f(x) = ix5 + (2 – i)x4 + (2 – 3i)x3  +  ix2 – 7 + 2i, g(x) = x – 3 – 2i;

4.14.

à) f(x) = 3õ7 + x6 + 2x5 – 5x4 + x3 + 3x27, g(x) = x – 1;
á) f(x) = ix5 + (1 + 2i)x4 + (1 – i)x3  +  ix2 + (1 + i)x +3, g(x) = x – 1 + i;

4.15.

à) f(x) = 4õ6 – 3x5 + 2x3 – 6x2 + x –3, g(x) = x + 3;
á) f(x) = ix6 – (2 + i)x4 + 3x2   2x – 7 + i, g(x) = x – 3i;

4.16.

à) f(x) = õ5 – 3x4 + 5x3 + 4x2 + 2x –10, g(x) = x – 1;
á) f(x) = (–1 + 2)x5 + (3 + i)x4 + (1 + 2i)x3  – (1 + i)x2 + (4 + i)x + 4 + i, g(x) = x – 1 – i;

4.17.

à) f(x) = 2õ5 + 3x4 + 4x3 + x21, g(x) = x – 1;
á) f(x) = x5 + (1 + 2i)x4 – (1 + 3i)x2  +7, g(x) = x – i;

4.18.

à) f(x) = õ5 + 2x4 – 3x3 + 2x2 – x –1, g(x) = x – 2;
á) f(x) = ix5 + ix4 – 2x3  + x2 + (1 – i)x +4, g(x) = x – 1 + i;

4.19.

à) f(x) = 2õ6 – 3x4 + 2x3 – x2 – 4x –3, g(x) = x – 3;
á) f(x) = ix5 +(1 + i)x4 + (5 + i)x3 – (1 – i)x2 + (3 + i)x + i +5, g(x) = x + 1 – i;

4.20.

à) f(x) = 2õ6 + 4x3 – 4x2 + 2x –4, g(x) = x + 1;
á) f(x) = x5 + ix4 – (–1 + i)x2 + 2 + i, g(x) = x – 1 + 2i;

4.21.

à) f(x) = 3õ6 – 2x5 – x3 – 4x +1, g(x) = x + 3;
á) f(x) = ix5 + (–2 + i)x4 – 3(–1 + i)x2 – (3 + i)x2 – (3 + i)x –2, g(x) = x – 1 + i;

4.22.  

à) f(x) = 4õ8 – 3x6 + 2x4 – 3x3 + 2x –6, g(x) = x + 2;
á) f(x) = ix6 – (1 + i)x5 + (1 – 2i)x3 + 2ix2 – 3(1 – i)x +1, g(x) = x – 2 – i;

4.23.

à) f(x) = 2õ8 – 3x7 + 4x5 – x3 + 4x +3, g(x) = x + 4;
á) f(x) = ix5 – (3 + i)x3 + 2ix2  – (4 + 2i)x + 14i, g(x) = x – 1 – i;

4.24.

à) f(x) = 2õ7 – 3x6 – 4x3 + 2x2 +3, g(x) = x + 5;
á) f(x) = 4x5 + (2 – i)x4 – 5ix3 + (1 + i)x – 2i, g(x) = x + 1 – i;

4.25.

à) f(x) = 3õ7 – 2x5 + 3x4 – 2x2 + x –6, g(x) = x – 4;
á) f(x) = 3ix5 + (3 – i)x4 + (4 – i)x3 + (1 – i)x2 + (2 – i)x – 2 + 6i, g(x) = x – 1 – i;

4.26.

à) f(x) = 15õ6 – 8x5 – 7x4 + x +3, g(x) = x – 2;
á) f(x) = 2ix5 – ix4 +  3x2  – ix +1, g(x) = x – 1 – i;

4.27.

à) f(x) = 5õ6 – 6x5 – 3x2 – 2x +1, g(x) = x + 4;
á) f(x) = 6x6 – 5x5  – ix3 + (1 + i)x +2, g(x) = x – 1 + i;

4.28.

à) f(x) = 4õ6 – 8x5 – 16x3 + 8x2 + 32x –64, g(x) = x – 0,5;
á) f(x) = 2x6  – ix5 + ix4 + 6x3 + 12x – 8 + 2i, g(x) = x + i;

4.29.

à) f(x) = 4õ5 – 6x4 + 5x3 – 2x +8, g(x) = x + 3;
á) f(x) = 4x6 + 6x4 – ix3 + (1 – i)x2 + 3x –16, g(x) = x – 2 – i;

4.30.

à) f(x) = 3õ7 – 4x5 + 2x4 – 6x3 + 2x +11, g(x) = x + 2;
á) f(x) = ix6  – 2x5 + (1 – i)x3  3x + 2 – 3i, g(x) = x + 2i;

4.31.

à) f(x) = 2õ7 + 2x6 – 3x3 + 6x2 – 7x +10, g(x) = x – 4;
á) f(x) = 2ix5 – ix4 +  3x2 – (2 +  3i)x – 7 + 2i, g(x) = x – 2 +  i;

4.32.

à) f(x) = 3õ7 + 8x6 – 4x4 + 2x2 + 6x +1, g(x) = x + 2;
á) f(x) = 2x8   ix7 + 5x5  – 2ix4 + (1 + i)x2 + 1 – 2i, g(x) = x – 1 + 2i;

4.33.

à) f(x) = 64õ6 + 32x3 – 8x2 – 72x +8, g(x) = x + 0,5;
á) f(x) = 6x5 – 7x4 + 3x3  – (2 + i)x2 – 3x + 4 – 3i, g(x) = x + 2 – i;

4.34.

à) f(x) = 8õ6 – 4x5 + 3x2 – 4x +7, g(x) = x + 4;
á) f(x) = 2x7   3x6 + (2 – i)x4  – ix3 – (1 + i)x + 3 – i, g(x) = x + 3 + i;

4.35.

à) f(x) = 2õ8 – 4x6 + 3x4 – 2x3 + 7x –12, g(x) = x + 3;
á) f(x) = 2x6   (1 + i)x5 – ix4  – 2x2 + 3 – 3i, g(x) = x – 2 + 2i;

4.36.

à) f(x) = 4õ7 – 2x5 + 3x3 – 4x2 – ix + 4 – 2i, g(x) = x – 4;
á) f(x) = 2x6 + (1 – i)x5 + 2ix4  – (3 + 2i)x2 – 3 + 5i, g(x) = x + 2 – 2i.

\.Ïðèìåð.\

 

                              Copyright © 2008-2009 Îâ÷èííèêîâ À.Â.  Ôèëèàë ÊÃÏÓ. Âñå ïðàâà çàùèùåíû.