x^16 - 81 :factor?
回答 (3)
2016-03-20 10:53 pm
x^16 - 81
= (x^8 + 9)(x^8 - 9)
= (x^8 + 9)(x^4 + 3)(x^4 - 3)
that is all for integers .. more factoring would require irrational numbers and complex numbers
= (x^8 + 9)(x^8 - 9)
= (x^8 + 9)(x^4 + 3)(x^4 - 3)
that is all for integers .. more factoring would require irrational numbers and complex numbers
2016-03-20 10:52 pm
[ x^4 - 9 ] [ x^4 + 9 ]
[ x^2 - 3 ] [ x^2 + 3 ] [ x^4 + 9 ]
[ x - √3 ] [ x + √3 ] [ x^2 + 3 ] [ x^4 + 9 ]
[ x^2 - 3 ] [ x^2 + 3 ] [ x^4 + 9 ]
[ x - √3 ] [ x + √3 ] [ x^2 + 3 ] [ x^4 + 9 ]
2016-03-20 11:00 pm
X^16 - 81
= (x^8)*2 - (9)^2
= (x^8 - 9)(x^8 + 9)
= [ (x^4)^2 - (9)^2](x^8 + 9)
= [ ( x^4 - 3)(x^4 + 3)](x^8 + 9)
= [ (x^2 - √3)(x^2 + √3)](x^4 + 3)(x^8 + 9)
= ( x - sqrt(√3))(x - sqrt(√3))(x^2 + √3)](x^4 + 3)(x^8 + 9)
= (x^8)*2 - (9)^2
= (x^8 - 9)(x^8 + 9)
= [ (x^4)^2 - (9)^2](x^8 + 9)
= [ ( x^4 - 3)(x^4 + 3)](x^8 + 9)
= [ (x^2 - √3)(x^2 + √3)](x^4 + 3)(x^8 + 9)
= ( x - sqrt(√3))(x - sqrt(√3))(x^2 + √3)](x^4 + 3)(x^8 + 9)
收錄日期: 2021-05-01 16:40:55
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20160320144729AAIxH30