Question

x^10+x^5+1因式分解

x^10+x^5+1因式分解要过程谢谢

Answer 1

x^10+x^5+1
=x^10+x^9-x^9+x^8-x^8+x^7-x^7+x^6-x^6+x^5-x^5+x^4-x^4+x^3-x^3+x^2-x^2+x-x+x^5+1
=x^10+x^9+x^8-x^9-x^8-x^7+x^7+x^6+x^5-x^6-x^5-x^4+x^5+x^4+x^3-x^3-x^2-x+x^2+x+1
=x^8(x^2+x+1)-x^7(x^2+x+1)+x^5(x^2+x+1)-x^4(x^2+x+1)+x^3(x^2+x+1)-x(x^2+x+1)+(x^2+x+1)
=(x^8-x^7+x^5-x^4+x^3-x+1)(x^2+x+1)

Answer 2

x^7+x^5+1=(x^2+x+1)(x^5-x^4+x^3-x+1)
x^7+x^5+1除以x^3-1余数得x^2+x+1,因为x^3-1=(x-1)(x^2+x+1)
提公因式x^2+x+1得：x^7+x^5+1=(x^2+x+1)(x^5-x^4+x^3-x+1)
江西桑海中学初二（5）班

Answer 3

x^10+x^5+1
=(x-1)(x^10+x^5+1)/(x-1)
=(x^11-x^10+x^6-x^5+x-1)/(x-1)
其中x^11-x^10+x^6-x^5+x-1
=(x^11-x^5)-(x^10-x)+(x^6-1)
=(x^6-1)(x^5+1)-x(x^9-1)
=(x^3-1)(x^3+1)(x^5+1)-x(x^3-1)(x^6+x^3+1)
=(x^3-1)[(x^8+x^5+x^3+1)-(x^7+x^4+x)]
=(x^3-1)(x^8-x^7+x^5-x^4+x^3-x+1)
∴原式=(x^3-1)(x^8-x^7+x^5-x^4+x^3-x+1)/(x-1)
=(x^2+x+1)(x^8-x^7+x^5-x^4+x^3-x+1)

Answer 4

x^10+x^5+1=(x^10+x^9+x^8)-x^9-x^8-x^7+(x^7+x^6+x^5)-x^6-x^5-x^4+(x^5+x^4+x^3)-x^3-x^2-x+(x^2+x+1)
=(x^2+x+1)(x^8-x^7+x^5-x^4+x^3-x+1)