X¹²-1 = Разделите на многочлены . Created by sonya031104. matematika-ru

X¹²-1 = Разделите на многочлены ...

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Ответ:

$x^{12}-1=(x^6)^2-1^2=(x^6-1)(x^6+1)=\Big((x^2)^3-1^3\Big)\Big((x^2)^3+1^3\Big)=\\\\=\Big((x^2-1)(x^4+x^2+1)\Big)\Big((x^2+1)(x^4-x^2+1)\Big)=\\\\=(x-1)(x+1)(x^4+x^2+1)(x^2+1)(x^4-x^2+1)=\\\\=(x-1)(x+1)(x^2+1-x)(x^2+1+x)(x^2+1)(x^4-x^2+1)\\\\\\\star \ \ x^4+x^2+1=(x^4+2x^2+1)-x^2=(x^2+1)^2-x^2=\\\\=(x^2+1-x)(x^2+1+x)\ \ \star$

2 votes Thanks 1

ZlataSergeeva2000

Решение:

x¹² - 1 = (x⁶ + 1) · (x⁶ - 1) = (х² + 1)(х⁴ - х² + 1) · (x³ + 1)(х³ - 1) =

= (х² + 1)(х⁴ - х² + 1) · (х + 1)(х² - х + 1) · (х - 1) (х² + х + 1)

0 votes Thanks 0

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