x^4 + x^2 + 1
[ sure not prime ! ]
[ help ] Factor Completely Please [ quick ]
2007-06-17 1:07 am
回答 (3)
2007-06-17 1:24 am
✔ 最佳答案
x^4 + x^2 + 1=x^4 + x^2 + x^2 + 1- x^2
=x^4 + 2x^2 + 1 - x^2
= ( x^2 + 1 ) ^2 - x^2
= ( x^2 + 1 + x )( x^2 + 1 - x)
= ( x^2 + x + 1 )( x^2 - x + 1)
參考: My Maths Knowledge
2007-06-17 1:28 am
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)
= (x^2 + x + 1)(x^2 - x + 1)
= x^4 + 2x^2 + 1 - x^2
= (x^2 + 1)^2 - x^2
= (x^2 + 1 + x)(x^2 + 1 - x)
= (x^2 + x + 1)(x^2 - x + 1)
2007-06-17 1:25 am
x^4 + x^2 + 1
=x^4 + 2(x^2) + 1-x^2
=(x^2+1)^2-(x)^2
=(x^2-x+1)(x^2+x+1) (由於a^2-b^2=(a-b)(a+b))
consider x^2-x+1
x^2-x+1
=(x-0.5)^2+0.75
if x equal to 0 or 1
x^2-x+1=1
if x doesn't equal to 0 or 1
x^2-x+1>1 and x^4 + x^2 + 1 is not a prime no.
=x^4 + 2(x^2) + 1-x^2
=(x^2+1)^2-(x)^2
=(x^2-x+1)(x^2+x+1) (由於a^2-b^2=(a-b)(a+b))
consider x^2-x+1
x^2-x+1
=(x-0.5)^2+0.75
if x equal to 0 or 1
x^2-x+1=1
if x doesn't equal to 0 or 1
x^2-x+1>1 and x^4 + x^2 + 1 is not a prime no.
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