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Консультация № 146048
05.10.2008, 04:56
0.00 руб.
0
1
1
Здравствуйте эксперты!
Помогите пожалуйста справиться с двумя примерами. Требуется найти многочлен А для которого верно равенство:
№1
х^5-32=А(х-2)
№2
х^7-128=А(х-2)
Спасибо.
Помогите пожалуйста справиться с двумя примерами. Требуется найти многочлен А для которого верно равенство:
№1
х^5-32=А(х-2)
№2
х^7-128=А(х-2)
Спасибо.
Обсуждение
Неизвестный
06.10.2008, 15:20
общий
это ответ
Здравствуйте, Qlejer!
Деление многочлена на многочлен записывается в столбик наподобие обычного деления чисел.
№1
х^5-32=А(х-2);
A=(х^5-32)/(х-2)
1) Делим первый член х^5 делимого на первый член х делителя; результат х^4 является первым членом частного.
2) Умножаем полученное выражение х^4 на делитель x-2 ; записываем результат х^5-2х^4 под делимым (один подобный член под другим).
3) Вычитаем почленно этот результат из делимого и сносим вниз следующий по порядку член делимого -32; получаем остаток 2х^4-32 .
4) Делим первый член 2х^4 этого выражения на первый член x делителя; результат 2х^3 – это второй член частного.
5) Умножаем этот второй член частного 2х^3 на делитель x-2 и вновь записываем результат 2х^4-4х^3 под делимым (один подобный член под другим).
и так продолжаем до тех пор, пока многочлен делителя и делимого не будет одной степени.
Ответ: №1 A=х^4+2х^3+4х^2+8x+16;
№2 A=х^6+2х^5+4х^4+8х^3+16х^2+32x+64.
Деление многочлена на многочлен записывается в столбик наподобие обычного деления чисел.
№1
х^5-32=А(х-2);
A=(х^5-32)/(х-2)
1) Делим первый член х^5 делимого на первый член х делителя; результат х^4 является первым членом частного.
2) Умножаем полученное выражение х^4 на делитель x-2 ; записываем результат х^5-2х^4 под делимым (один подобный член под другим).
3) Вычитаем почленно этот результат из делимого и сносим вниз следующий по порядку член делимого -32; получаем остаток 2х^4-32 .
4) Делим первый член 2х^4 этого выражения на первый член x делителя; результат 2х^3 – это второй член частного.
5) Умножаем этот второй член частного 2х^3 на делитель x-2 и вновь записываем результат 2х^4-4х^3 под делимым (один подобный член под другим).
и так продолжаем до тех пор, пока многочлен делителя и делимого не будет одной степени.
Ответ: №1 A=х^4+2х^3+4х^2+8x+16;
№2 A=х^6+2х^5+4х^4+8х^3+16х^2+32x+64.
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