§ 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 + 3x² –2, 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 + x² –5, 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 + 3x² –7, 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 + x² –1, 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.

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