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ilya1806
@ilya1806
June 2022
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x^5 + x + 1 разложить на множетели
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Tanglee2
Используем формулу a^3 - b^3 = (a - b) * (a^2 + a * b + b^2)
x^5 + x + 1 = x^5 - x^2 + x^2 + x + 1 = x^2 * (x^3 - 1) + x^2 + x + 1 =
= x^2 * (x^3 - 1^3) + x^2 + x + 1 = x^2 * (x - 1) * (x^2 + x + 1) + (x^2 + x + 1) =
= (x^2 + x + 1) * (x^2 * (x - 1) + 1) = (x^2 + x + 1) * (x^3 - x^2 + 1)
3 votes
Thanks 1
smirnov1779miron
x^5+x+1=x^5+x^4+x^3-x^4-x^3-x^2+x^2+x+1=x^3(x^2+x+1)-x^2(x^2+x+1)+(x^2+x+1)=(x^2+x+1)(x^3-x^2+1)решение на этот вопрос
1 votes
Thanks 1
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Answers & Comments
x^5 + x + 1 = x^5 - x^2 + x^2 + x + 1 = x^2 * (x^3 - 1) + x^2 + x + 1 =
= x^2 * (x^3 - 1^3) + x^2 + x + 1 = x^2 * (x - 1) * (x^2 + x + 1) + (x^2 + x + 1) =
= (x^2 + x + 1) * (x^2 * (x - 1) + 1) = (x^2 + x + 1) * (x^3 - x^2 + 1)