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à¤Ã×èͧÁ×ͧ͢ËÑÇ¢éÍ ¤é¹ËÒã¹ËÑÇ¢é͹Õé
  #1  
Old 31 ¡Ã¡®Ò¤Á 2009, 16:47
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¨§á¡µÑÇ»ÃСͺ¢Í§
$$5x^4-36x^3-52x^2+72x+20$$
µÍº¾ÃéÍÁÍéÒ§ÍÔ§¢éͤÇÒÁ¹Õé
  #2  
Old 31 ¡Ã¡®Ò¤Á 2009, 17:01
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Scylla_Shadow Scylla_Shadow äÁèÍÂÙèã¹Ãкº
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ÍéÒ§ÍÔ§:
¢éͤÇÒÁà´ÔÁà¢Õ¹â´Â¤Ø³ sharkyboy View Post
¨§á¡µÑÇ»ÃСͺ¢Í§
$$5x^4-36x^3-52x^2+72x+20$$

$5x^4-36x^3-52x^2+72x+20=(x^2-8x-2)(5x^2+4x-10)$
µÍº¾ÃéÍÁÍéÒ§ÍÔ§¢éͤÇÒÁ¹Õé
  #3  
Old 31 ¡Ã¡®Ò¤Á 2009, 18:07
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555+ à¾Ôè§ÊͺÇѹ¹Õéàͧ ⨷Â×Áѹ·ÐáÁè§æ ÍФÃѺ à¤éҺ͡ãËéãªé·ÄÉ®ÕàÈÉàËÅ×Í

»Å.¤Ø³ sharky boy ÍÂÙè ¹Ç. »Ð¤ÃѺ
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1 = 2 ä´é 555+
ÁѹäÁèÁÕÍÐäÃá¹è¹Í¹ 555+
µÍº¾ÃéÍÁÍéÒ§ÍÔ§¢éͤÇÒÁ¹Õé
  #4  
Old 31 ¡Ã¡®Ò¤Á 2009, 18:19
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äÁè¹èÒ¨Ðãªé·ÄÉ®ÕàÈÉàËÅ×Íä´é¤ÃѺ
µÍº¾ÃéÍÁÍéÒ§ÍÔ§¢éͤÇÒÁ¹Õé
  #5  
Old 31 ¡Ã¡®Ò¤Á 2009, 18:45
ÍÂÒ¡à¡è§àÅ¢¤ÃѺ's Avatar
ÍÂÒ¡à¡è§àÅ¢¤ÃѺ ÍÂÒ¡à¡è§àÅ¢¤ÃѺ äÁèÍÂÙèã¹Ãкº
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¾Ç¡·ÕèãËéᡵÑÇ»ÃСͺËÅÒÂ澨¹ìÍÂèÒ§¹Õé

¾Í¨ÐÁÕÇÔ¸Õ·ÓËÃ×ÍÇÔ¸ÕÁͧ§èÒÂæäËÁ¤ÃѺ

à¾ÃÒÐÁѹÂÒ¡ÁÒ¡·Õè¨Ð¹Ö¡àÅ¢ÍÍ¡ÁÒ

»Å.äÁèàÍÒÇÔ¸Õ¤Ù³¡ÃШÒ¨ҡªé͹ФÃѺ
µÍº¾ÃéÍÁÍéÒ§ÍÔ§¢éͤÇÒÁ¹Õé
  #6  
Old 31 ¡Ã¡®Ò¤Á 2009, 18:57
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¨Ñº¤Ùè µÑÇ¡ÓÅѧ 4 ¡ÑºµÑÇÊØ´·éÒ ãªéà¾ÔèÁ¾¨¹ì¡ÅÒ§
áÅéÇàÍÒ¡ÓÅѧ 3 ¤Ùè ¡ÓÅѧ 1 Åͧ´Ö§æ´Ù¤ÃѺ
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1 = 2 ä´é 555+
ÁѹäÁèÁÕÍÐäÃá¹è¹Í¹ 555+
µÍº¾ÃéÍÁÍéÒ§ÍÔ§¢éͤÇÒÁ¹Õé
  #7  
Old 31 ¡Ã¡®Ò¤Á 2009, 20:12
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ÍéÒ§ÍÔ§:
¢éͤÇÒÁà´ÔÁà¢Õ¹â´Â¤Ø³ ÍÂÒ¡à¡è§àÅ¢¤ÃѺ View Post
¾Ç¡·ÕèãËéᡵÑÇ»ÃСͺËÅÒÂ澨¹ìÍÂèÒ§¹Õé

¾Í¨ÐÁÕÇÔ¸Õ·ÓËÃ×ÍÇÔ¸ÕÁͧ§èÒÂæäËÁ¤ÃѺ

à¾ÃÒÐÁѹÂÒ¡ÁÒ¡·Õè¨Ð¹Ö¡àÅ¢ÍÍ¡ÁÒ

»Å.äÁèàÍÒÇÔ¸Õ¤Ù³¡ÃШÒ¨ҡªé͹ФÃѺ
ÇÔ¸Õ§èÒÂæ·Õè¼ÁÃÙé(ÊÓËÃѺ¾ËعÒÁ¡ÓÅѧ4¹Ð¤ÃѺ) ¤×ÍËÅѧ¨Ò¡·ÕèàÃÒÅͧãªé·ÄÉ®ÕàÈÉàËÅ×Í ¨¹ËÒÃÒ¡äÁèà¨ÍáÅéÇ
àÃÒ¡çÅͧà´ÒÇèÒÁѹÍÒ¨¨Ðá¡ä´éà»ç¹ $5x^4-36x^3-52x^2+72x+20=(ax^2+bx+c)(px^2+qx+r)$
áÅéÇàÃÒ¡çà·ÕºÊÑÁ»ÃÐÊÔ·¸Ôì¤ÃѺ ¨ÃÔ§æáÅéÇàÃÒÊÒÁÒöàÅ×Í¡ãËé $a=1$ ä»àÅÂä´é àËÁ×͹¡ÑºÇèÒàÃÒ·ÓÍÂèÒ§¹Õé $(ax^2+bx+c)(px^2+qx+r)=(x^2+\frac{b}{a}x+\frac{c}{a})(apx^2+aqx+ar)=(x^2+Bx+C)(Px^2+Qx+R)$

¤ÓµÍº $5x^4-36x^3-52x^2+72x+20=(x^2-8x-2)(5x^2+4x-10)$
·ÓãËéàÃÒàËç¹ÇèÒÃÒ¡¢Í§¾ËعÒÁ¹ÕéäÁèãªè¨Ó¹Ç¹µÃáÂÐ à¾ÃÒЩйÑé¹àÃÒãªéÇÔ¸ÕàÈÉàËÅ×ÍäÁèä´é
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µÍº¾ÃéÍÁÍéÒ§ÍÔ§¢éͤÇÒÁ¹Õé
  #8  
Old 31 ¡Ã¡®Ò¤Á 2009, 20:46
ÍÂÒ¡à¡è§àÅ¢¤ÃѺ's Avatar
ÍÂÒ¡à¡è§àÅ¢¤ÃѺ ÍÂÒ¡à¡è§àÅ¢¤ÃѺ äÁèÍÂÙèã¹Ãкº
¨ÍÁÂØ·¸ì˹éÒË¡
 
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#7

¢Íº¤Ø³ÁÒ¡¤ÃѺ

¶éÒà»ç¹ä»ä´é¼Áú¡Ç¹¢Í⨷ÂìᡵÑÇ»ÃСͺ
á¹Ç¹Õé˹èͤÃѺ ÍÂÒ¡½Ö¡»ÃÐʺ¡Òóì
µÍº¾ÃéÍÁÍéÒ§ÍÔ§¢éͤÇÒÁ¹Õé
  #9  
Old 31 ¡Ã¡®Ò¤Á 2009, 21:08
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Scylla_Shadow Scylla_Shadow äÁèÍÂÙèã¹Ãкº
ÅÁ»ÃÒ³äÃéÊÀÒ¾
 
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ÍéÒ§ÍÔ§:
¢éͤÇÒÁà´ÔÁà¢Õ¹â´Â¤Ø³ ÍÂÒ¡à¡è§àÅ¢¤ÃѺ View Post
...
¶éÒà»ç¹ä»ä´é¼Áú¡Ç¹¢Í⨷ÂìᡵÑÇ»ÃСͺ
á¹Ç¹Õé˹èͤÃѺ ÍÂÒ¡½Ö¡»ÃÐʺ¡Òóì
¨§á¡µÑÇ»ÃСͺµèÍ仹Õé

1.$2x^6+5x^5+11x^4+14x^3+16x^2+8x+4$

2.$x^4+3x^3+6x^2+5x+3$

3.$4x^4+13x^3+28x^2+27x+18$

4.$-18x^4+27x^3-28x^2+13x-4$

5.$333x^4+666x^3+888x^2-222x-333$

6.$3456x^4-54$

7.$3456x^4+432x^3+456x^2-54x-111$

»ÃÐÁÒ³¹Õéä´éäËÁ¤ÃѺ
µÍº¾ÃéÍÁÍéÒ§ÍÔ§¢éͤÇÒÁ¹Õé
  #10  
Old 31 ¡Ã¡®Ò¤Á 2009, 22:14
ÍÂÒ¡à¡è§àÅ¢¤ÃѺ's Avatar
ÍÂÒ¡à¡è§àÅ¢¤ÃѺ ÍÂÒ¡à¡è§àÅ¢¤ÃѺ äÁèÍÂÙèã¹Ãкº
¨ÍÁÂØ·¸ì˹éÒË¡
 
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#9

¢Íº¤Ø³ÍÂèÒ§ÊÙ§¤ÃѺ
µÍº¾ÃéÍÁÍéÒ§ÍÔ§¢éͤÇÒÁ¹Õé
  #11  
Old 31 ¡Ã¡®Ò¤Á 2009, 23:01
ÍÂÒ¡à¡è§àÅ¢¤ÃѺ's Avatar
ÍÂÒ¡à¡è§àÅ¢¤ÃѺ ÍÂÒ¡à¡è§àÅ¢¤ÃѺ äÁèÍÂÙèã¹Ãкº
¨ÍÁÂØ·¸ì˹éÒË¡
 
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·ÓäÁÁѹÂÒ¡ÍÂèÒ§¹Õé TT

¤Ô´äÁèÍÍ¡ ÁÖ¹µÖº
µÍº¾ÃéÍÁÍéÒ§ÍÔ§¢éͤÇÒÁ¹Õé
  #12  
Old 01 ÊÔ§ËÒ¤Á 2009, 09:06
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plalasy plalasy äÁèÍÂÙèã¹Ãкº
ËÑ´à´Ô¹ÅÁ»ÃÒ³
 
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¢éÍ·Õè¼Á¶ÒÁä»à¹ÕèÂ
¼Á¡ç·ÓÇÔ¸Õ¡ÓÅѧÊͧÊÑÁºÙó×仡è͹¹èФÃѺ
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µÍº¾ÃéÍÁÍéÒ§ÍÔ§¢éͤÇÒÁ¹Õé
  #13  
Old 01 ÊÔ§ËÒ¤Á 2009, 09:11
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sharkyboy sharkyboy äÁèÍÂÙèã¹Ãкº
ÅÁ»ÃÒ³ºÃÔÊØ·¸Ôì
 
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ÊÓËÃѺ¹Ñ¡àÃÕ¹ ¹Ç.¹Ð¤ÃѺ
Í.àªÒÇìºÍ¡ÇèÒ ¢é͹Õè¿ÃչФÃѺ
à¾ÃÒÐÍ.à©ÅÔÁªÑ ÍÍ¡¢éÍÊͺ¼Ô´¤ÃѺ
¼Á¡çà»ç¹Ë¹Öè§ã¹ ¹Ç.¹èФÃѺ
math_lnw ÍÂÙè ¹Ç.ËÃͤÃѺ Ëéͧä˹ËÃͤÃѺ
¼ÁÍÂÙè 3/1 ¹èФÃѺ
¢é͹Õé¼Á¡çµÍºä»ÇèÒäÁèÊÒÁÒöá¡ä´é áµè¡çáÊ´§ÇÔ¸Õ·ÓẺÍ×è¹ãËé´Ù¹èФÃѺ...
ÊÃØ»¤×Í ¿ÃÕ¤ÃÕº
µÍº¾ÃéÍÁÍéÒ§ÍÔ§¢éͤÇÒÁ¹Õé
  #14  
Old 01 ÊÔ§ËÒ¤Á 2009, 10:25
¤usÑ¡¤³Ôm's Avatar
¤usÑ¡¤³Ôm ¤usÑ¡¤³Ôm äÁèÍÂÙèã¹Ãкº
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ÍéÒ§ÍÔ§:
¢éͤÇÒÁà´ÔÁà¢Õ¹â´Â¤Ø³ Scylla_Shadow View Post
¨§á¡µÑÇ»ÃСͺµèÍ仹Õé

1.$2x^6+5x^5+11x^4+14x^3+16x^2+8x+4$

2.$x^4+3x^3+6x^2+5x+3$

3.$4x^4+13x^3+28x^2+27x+18$

4.$-18x^4+27x^3-28x^2+13x-4$

5.$333x^4+666x^3+888x^2-222x-333$

6.$3456x^4-54$

7.$3456x^4+432x^3+456x^2-54x-111$

»ÃÐÁÒ³¹Õéä´éäËÁ¤ÃѺ
1. $(x^2+2)(x^2+2x+2)(2x^2+x+1)$
6.$54(8x^2-1)(8x^2+1)$

ÃÖà»ÅèÒ
__________________
µÍº¾ÃéÍÁÍéÒ§ÍÔ§¢éͤÇÒÁ¹Õé
  #15  
Old 01 ÊÔ§ËÒ¤Á 2009, 11:00
banker banker äÁèÍÂÙèã¹Ãкº
à·¾à«Õ¹
 
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$5x^4-36x^3-52x^2+72x+20$

= $(x^2-8 x-2) (5 x^2+4 x-10)$




1.$2x^6+5x^5+11x^4+14x^3+16x^2+8x+4$

= $(x^2+2) (x^2+2 x+2) (2 x^2+x+1)$



2.$x^4+3x^3+6x^2+5x+3$

=$(x^2+x+1) (x^2+2 x+3)$



3.$4x^4+13x^3+28x^2+27x+18$

=$(x^2+2 x+3) (4 x^2+5 x+6)$



4.$-18x^4+27x^3-28x^2+13x-4$

=$-(3 x^2-2 x+1) (6 x^2-5 x+4)$



5.$333x^4+666x^3+888x^2-222x-333$

=$111 (x^2+2 x+3) (3 x^2-1)$



6.$3456x^4-54$

=$54 (8 x^2-1) (8 x^2+1)$



7.$3456x^4+432x^3+456x^2-54x-111$

=$3 (8 x^2-1) (144 x^2+18 x+37)$


àÍÒà©ÅÂÁÒãËé
áÅéÇÅͧ·ÓÂé͹¨Ò¡¤ÓµÍºä»ËÒ⨷Âì´Ù¤ÃѺ
µÑÇÍÂèÒ§¢éÍ 6. Åͧ·ÓÂé͹¢Öé¹ä» ¡ç¨ÐàËç¹á¹Ç·Ò§àͧ¤ÃѺ ½Ö¡·ÓºèÍÂæ ´Ç§µÒ¨ÐàË繸ÃÃÁ

6.$3456x^4-54$

= $54(64x^4-1)$

=$54[(8x^2)^2-(1)^2]$

=$54 (8 x^2-1) (8 x^2+1)$
__________________
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