การแยกต, วประกอบ, บทความน, ไม, การอ, างอ, งจากแหล, งท, มาใดกร, ณาช, วยปร, บปร, งบทความน, โดยเพ, มการอ, างอ, งแหล, งท, มาท, าเช, อถ, เน, อความท, ไม, แหล, งท, มาอาจถ, กค, ดค, านหร, อลบออก, เร, ยนร, าจะนำสารแม, แบบน, ออกได, อย, างไรและเม, อไร, งกฤษ, factorization. bthkhwamniimmikarxangxingcakaehlngthimaidkrunachwyprbprungbthkhwamni odyephimkarxangxingaehlngthimathinaechuxthux enuxkhwamthiimmiaehlngthimaxacthukkhdkhanhruxlbxxk eriynruwacanasaraemaebbnixxkidxyangiraelaemuxir karaeyktwprakxb xngkvs factorization inthangkhnitsastr hmaythungkaraebngyxywtthuthangkhnitsastr echn canwn phhunam hruxemthriks ihxyuinrupphlkhunkhxngwtthuxun sungemuxkhuntwprakxbehlannekhadwykncaidphllphthdngedim twxyangechn canwn 15 samarthaeyktwprakxbihepncanwnechphaaidepn 3 5 aelaphhunam x 2 4 displaystyle x 2 4 samarthaeykidepn x 2 x 2 displaystyle x 2 x 2 epntncanwnechingsxn xngkvs complex number inthangkhnitsastr khux estthitxetimcakestkhxngcanwncringodyephimcanwn i displaystyle i sungthaihsmkar i 2 1 0 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sungimmiwithiidthisamarthaeyktwprakxbcanwnkhnadihyidxyangrwderw aetkhwamyungyakniepnpraoychntxkarrksakhwamplxdphyinkhntxnwithikhxngkarekharhslbaebbkuyaecxsmmatr xyangechn RSAsahrbkaraeyktwprakxbkhxngemthrikseriykwa karaeykemthriks matrix decomposition sungmiwithikarthiehmaasmaetktangknipsahrbemthriksnn echn karaeykaebbkhiwxar QR decomposition epntn withihlkxyanghnungthiniymkhuxkarthaihepnphlkhunkhxng emthriksechingtngchak orthogonal matrix hruxemthriksyuniaethri unitary matrix kbemthriksaebbsamehliym triangular matrix xiktwxyanghnungkhxngkaraeyktwprakxbkhuxkaraeykfngkchnihklayepnkarprakxbfngkchn function composition kbfngkchnxunodymienguxnikhthiecaacng twxyangenguxnikhechn fngkchnthukfngkchnsamarthekhiynihxyuinrupkhxngkarprakxbkhxngfngkchnthwthung surjective function kbfngkchnhnungtxhnung injective function epntn enuxha 1 canwnetm 2 phhunam 2 1 karaeyktwprakxbphhunamkalngsxng 2 1 1 phhunamthisamarthaeykidbncanwnetm 2 1 2 itrnamkalngsxngsmburn 2 1 3 phlbwkaelaphltangkalngsxng 2 2 karaeyktwprakxbphhunamxun 2 2 1 phlbwkaelaphltangkalngsamcanwnetm aekikhdubthkhwamhlkthi karaeyktwprakxbcanwnetmphhunam aekikhkaraeyktwprakxbphhunamkalngsxng aekikh phhunamkalngsxngid bncanwnechingsxn khuxphhunamthixyuinrup a x 2 b x c displaystyle ax 2 bx c emux a b c C displaystyle a b c in mathbb C samarthaeyktwprakxbihepnniphcnthixyuinrup a x a x b displaystyle a x alpha x beta emux a displaystyle alpha aela b displaystyle beta khuxrakkhxngphhunam sungkhanwnidcaksutrkalngsxngdngni a x 2 b x c a x a x b a x b b 2 4 a c 2 a x b b 2 4 a c 2 a displaystyle ax 2 bx c a x alpha x beta a left x left frac b sqrt b 2 4ac 2a right right left x left frac b sqrt b 2 4ac 2a right right dd phhunamthisamarthaeykidbncanwnetm aekikh bangkhrngphhunamkalngsxngsamarthaeykxxkidepnthwinam binomial sxngtwdwysmprasiththithiepncanwnetm odyimcaepntxngichsutrkalngsxnginkarkhanwn sungmipraoychnsahrbkarharakkhxngsmkarkalngsxng odythiphhunam a x 2 b x c displaystyle ax 2 bx c dd samarthaeykidepn m x p n x q displaystyle mx p nx q dd emux m n a displaystyle mn a p q c displaystyle pq c p n m q b displaystyle pn mq b dd caknncungihthwinamaetlatwethakbsuny aelwkhanwnhakhakhxng x ephuxharakkhxngsmkarkalngsxng itrnamkalngsxngsmburn aekikh aephnphaphthiphisucnwa a b a 2ab b phhunamkalngsxngbangchnidsamarthaeyktwprakxbxxkidepnthwinamthiehmuxnkn phhunamnneriykwa itrnamkalngsxngsmburn hruxephiyngaekh kalngsxngsmburn sungphhunamdngklawsamarthaeykiddngni a b 2 a b a b a 2 2 a b b 2 displaystyle a b 2 a b a b a 2 2ab b 2 a b 2 a b a b a 2 2 a b b 2 displaystyle a b 2 a b a b a 2 2ab b 2 dd phlbwkaelaphltangkalngsxng aekikh dubthkhwamhlkthi phltangkalngsxng karaeyktwprakxbthangphichkhnitxikxyanghnungeriykwa phltangkalngsxng misutrdngni a 2 b 2 a b a b displaystyle a 2 b 2 a b a b dd sungepncringsahrbthngsxngphcn imwacanwnehlanncaepnkalngsxngsmburnhruxim thaphcnthngsxnglbkn kihaethndwysutrdngklawidthnthi aetthaphcnthngsxngbwkkn thwinamthiidcakkaraeyktwprakxbcatxngmicanwncintphaphekhamaekiywkhxng sungaesdngiddngni a 2 b 2 a b i a b i displaystyle a 2 b 2 a bi a bi dd twxyangechn 4 x 2 49 displaystyle 4x 2 49 samarthaeykidepn 2 x 7 i 2 x 7 i displaystyle 2x 7i 2x 7i epntn karaeyktwprakxbphhunamxun aekikh phlbwkaelaphltangkalngsam aekikh sutrsahrbkaraeyktwprakxbkhxngphlbwkaelaphltangkalngsamepndngni phlbwkaelaphltangsamarthaeyktwprakxbepn a 3 b 3 a b a 2 a b b 2 displaystyle a 3 b 3 a b a 2 ab b 2 a 3 b 3 a b a 2 a b b 2 displaystyle a 3 b 3 a b a 2 ab b 2 echn x3 103 or x3 1000 samarthaeyktwprakxbepn x 10 x2 10x 100 bthkhwamekiywkbkhnitsastrniyngepnokhrng khunsamarthchwywikiphiediyidodyephimkhxmul duephimthi sthaniyxy khnitsastrekhathungcak https th wikipedia org w index php title karaeyktwprakxb amp oldid 9455089, wikipedia, วิกิ หนังสือ, หนังสือ, ห้องสมุด,