Factorize:
1)x^8-16
2)x^3+x^6+x^9+x^12
請列明步驟
Factorization
2008-01-21 3:44 am
回答 (2)
2008-01-21 4:03 am
✔ 最佳答案
1.x^8-16
=x^8-2^4
=(x^4+2^2)(x^4-2^2)
=(x^4+4)(x^2+2)(x^2-2)
=(x^4+4x^2+4-4x^2)(x^2+2)(x^2-2)
=〔(x^4+4x^2+4)-(2x)^2〕(x^2+2)(x^2-2)
=〔(x^2+2)^2-(2x)^2〕(x^2+2)(x^2-2)
=(x^2+2x+2)(x^2-2x+2)(x^2+2)(x^2-2)
2.
x^3+x^6+x^9+x^12
=x^3(x^9+x^6+x^3+1)
=x^3〔x^6(x^3+1)+(x^3+1)〕
=x^3(x^6+1)(x^3+1)
=x^3(x^2+1)(x^4-x^2+1)(x+1)(x^2-x+1)
參考: me
2008-01-21 4:10 am
1)x^8-16
= (X^4)^2-4^2 (張佢正成 a^2 - b^2)
= (x^4 - 4)(x^4 +4) (a^2-b^2 = (a+b)(a-b))
2)x^3+x^6+x^9+x^12
=x^3( 1+ x^3 +x^6 +x^9) (張x^3抽出, 咁就會變成一舊野成一舊野喇 !)
= (X^4)^2-4^2 (張佢正成 a^2 - b^2)
= (x^4 - 4)(x^4 +4) (a^2-b^2 = (a+b)(a-b))
2)x^3+x^6+x^9+x^12
=x^3( 1+ x^3 +x^6 +x^9) (張x^3抽出, 咁就會變成一舊野成一舊野喇 !)
參考: me
收錄日期: 2021-04-14 19:00:12
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20080120000051KK03568