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小 發表於 2014-11-23 12:51 AM (第 3436 天)
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Q1a) x^128 - x^64
= x^64 (x^64 - 1)
= x^64 (x^32 + 1) (x^32 - 1)
= x^64 (x^32 + 1) (x^16 + 1) (x^16 - 1)
= x^64 (x^32 + 1) (x^16 + 1) (x^8 + 1) (x^8 - 1)
= x^64 (x^32 + 1) (x^16 + 1) (x^8 + 1) (x^4 + 1) (x^4 - 1)
= x^64 (x^32 + 1) (x^16 + 1) (x^8 + 1) (x^4 + 1) (x^2 + 1) (x^2 - 1)
= x^64 (x^32 + 1) (x^16 + 1) (x^8 + 1) (x^4 + 1) (x^2 + 1) (x + 1) (x - 1)
Q1b) x^128 = x^64
0 = x^128 - x^64
0 = x^64 (x^32 + 1) (x^16 + 1) (x^8 + 1) (x^4 + 1) (x^2 + 1) (x + 1) (x - 1)
x = 0 or x + 1 = 0 or x - 1 = 0
x = 0 or x = -1 or x = 1
Q2) 6x^5 + 6x^4 + 6
= 6 (x^5 + x^4 + 1)
= 6 [x^3 (x^2 + x + 1) - (x^3 - 1)]
= 6 [x^3 (x^2 + x + 1) - (x - 1) (x^2 + x + 1)]
= 6 {[x^3 - (x - 1)] (x^2 + x + 1)}
= 6 (x^3 - x + 1) (x^2 + x + 1)
