|
§ 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.
\.Ïðèìåð.\
|