§ 1. Многочлены над областью целостности

     № 7. С помощью схемы Горнера установите кратность

корня х₀ = с многочлена f(x).

7.01.

 f(x) = x⁵ – 2x⁴ + 4x³ – 28x² + 48x – 16, x₀ = 2;

7.02.

 f(x) = x⁴ – 2x³ + 5x² – 28x + 36, x₀ = 2;

7.03.

 f(x) = x⁵ – 3x⁴ – x³ + 11x² – 12x + 4, x₀ = 1;

7.04.

 f(x) = x⁵ – 6x⁴ + 13x³ – 14x² + 12x – 8, x₀ = 2;

7.05.

 f(x) = x⁴ + 8x³ – x² – 68x – 84, x₀ = –2;

7.06.

 f(x) = x⁵ – 6x⁴ + 13x³ – 14x² + 12x – 8, x₀ = 2;

7.07.

 f(x) = x⁴ – 2x³ + 2x² – 2x + 1, x₀ = 1;

7.08.

 f(x) = x⁵ – 6x⁴ + 11x³ – 2x² – 12x + 8, x₀ = 2;

7.09.

 f(x) = x⁵ – 8x⁴ + 21x³ – 27x² + 54x – 81, x₀ = 3;

7. 10.

 f(x) = x⁵ – 6x⁴ + 13x³ – 14x² + 12x – 8, x₀ = 2;

7.11.

 f(x) = x⁶ – 4x⁵ – 8x⁴ + 62x² + 96x – 72, x₀ = 2;

7.12.

 f(x) = x⁵ + 4x⁴ + 7x³ + 7x² + 4x + 1, x₀ = –1;

7.13.

 f(x) = 2x⁵ – 4x⁴ + x³ + x² – 1, x₀ = 1;

7.14.

 f(x) = 3x⁶ – 19x⁵ + 33x⁴ + 23x³ – 130x² – 132x – 40, x₀ = 2;

7.15.

 f(x) = x⁶ + 6x⁵ – 21x⁴ + 7x³ – x² + 8 , x₀ = 2;

7.16.

 f(x) = x⁶ – 6x⁵ + 12x⁴ – 5x³ – 18x² + 36x – 24, x₀ = 2;

7.17.

 f(x) = 3x⁶ – 5x⁵ + 3x⁴ – 7x³ + 2x² + 10x – 6, x₀ = 1;

7.18.

 f(x) = –x⁶ + 6x⁵ – 12x⁴ + 5x³ + 18x² – 36x + 24, x₀ = 2;

7.19.

 f(x) = x⁶ – 9x⁵ + 27x⁴ – 39x³ + 108x² – 32x + 324, x₀ = 3;

7.20.

 f(x) = x⁶ – 5x⁵ + 5x⁴ + 6x³ + 4x² – 40x + 32, x₀ = 2;

7.21.

 f(x) = 2x⁶ – 20x⁵ + 66x⁴ – 67x³ + 9x² – 189x + 351, x₀ = 3;

7.22.

 f(x) = x⁵ – 17x⁴ + 94x³ – 190x² + 161x – 49, x₀ = 1;

7.23.

 f(x) = x⁶ – 2x⁵ + 3x⁴ – 5x³ – 12x² + 2x – 1, x₀ = 2;

7.24.

 f(x) = x⁶ – 6x⁵ + 12x⁴ – 5x³ – 18x² + 36x – 24, x₀ = 2;

7.25.

 f(x) = –3x⁶ + 4x⁵ + 3x⁴ + x³ + 2x² – 4x + 8, x₀ = 2;

7.26.

 f(x) = x⁶ – 14x⁵ + 72x⁴ – 188x³ + 464x² – 1344x + 1792, x₀ = 4;

7.27.

 f(x) = x⁶ + 3x⁵ + 3x⁴ – x³ – 6x² – 6x – 2, x₀ = –1;

7.28.

 f(x) = x⁵ – 3x⁴ + 4x³ – 4x² + 3x – 1, x₀ = 1;

7.29.

 f(x) = –x⁵ + 2x⁴ – 3x³ + x² + 4x – 3, x₀ = 1;

7.30.

 f(x) = 2x⁵ – 6x⁴ + 7x³ – 5x² + 3x – 1, x₀ = 1;

7.31.

 f(x) = x⁶ – 2x⁴ + x³ – 4x² – 8x + 4, x₀ = 1;

7.32.

 f(x) = x⁵ – 12x⁴ + 49x³ – 76x² + 48x – 64, x₀ = 4;

7.33.

 f(x) = x⁵ – 6x⁴ + 11x³ – 2x² – 12x + 8, x₀ = 2;

7.34.

 f(x) = 4x⁵ + 12x⁴ + x³ + 6x² + 10x + 3, ;

7.35.

 f(x) = 3x⁵ – 18x⁴ + 41x³ – 54x² + 60x – 40, x₀ = 2;

7.36.

 f(x) = x⁵ – 6x⁴ + 13x³ – 14x² + 12x – 8, x₀ = 2.

\.Пример.\