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Консультация № 189756
10.09.2016, 21:46
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Уважаемые эксперты! Пожалуйста, помогите с решением задачи № 5 :
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Обсуждение
11.09.2016, 14:36
общий
это ответ
Здравствуйте, anton74551!
Имеем
3x2 + 8x - 3 = 3(x - 1/3)(x + 3).
Представим F(x) в виде:
P(x)*3(x-1/3)(x+3) + r(x),
где r(x) остаток от деления F(x) на 3x2 + 8x - 3.
Деление r(x) на (x + 3) должно дать остаток 1/2, а деление на (x - 1/3) -- остаток 2.
Положим r(x) = ax + b, т.к. остаток -- многочлен первой степени. Имеем
ax + b = [$945$]*(x+3) + 1/2,
ax + b = [$223$]*(x - 1/3) + 2.
Сравнивая коэффициенты при одинаковых степенях, получим
a = [$945$] = [$946$],
b = 3a + 1/2 = -a/3 +2.
Отсюда находим
a = 9/20, b = 37/20,
т.е., искомый остаток (9x + 37)/20.
Имеем
3x2 + 8x - 3 = 3(x - 1/3)(x + 3).
Представим F(x) в виде:
P(x)*3(x-1/3)(x+3) + r(x),
где r(x) остаток от деления F(x) на 3x2 + 8x - 3.
Деление r(x) на (x + 3) должно дать остаток 1/2, а деление на (x - 1/3) -- остаток 2.
Положим r(x) = ax + b, т.к. остаток -- многочлен первой степени. Имеем
ax + b = [$945$]*(x+3) + 1/2,
ax + b = [$223$]*(x - 1/3) + 2.
Сравнивая коэффициенты при одинаковых степенях, получим
a = [$945$] = [$946$],
b = 3a + 1/2 = -a/3 +2.
Отсюда находим
a = 9/20, b = 37/20,
т.е., искомый остаток (9x + 37)/20.
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