Ama-polynomials ama-factor

Ukufaka iqiniso enkulumweni ye-algebra inqubo okuyiyona, le nkulumo ibhalwe njengokuphindaphinda. Lapho ukufaka ama-polynomials lokho okuhlosiwe thola izici ezimbili noma ngaphezulu ezinenkulumo efanayo ye-algebra njengomkhiqizo.

Inhloso yokufaka ama-polynomials ukukwazi ukumela i-polynomial njenge umkhiqizo wamanye ama-polynomials amaningi asezingeni elincane.

I-Los izici zesisho se-algebra yimigomo noma izingxenye ezifanayo. Okubalulekile ukuthi uma ziphindaphindana zinikeza umphumela olingana nesisho sokuqala. Lokhu kungabonakala esibonelweni:

Isisho se-Algebra: x (x + y)

Ngokuphindaphinda imigomo komunye nomunye, sine: x² +xy

Ngakho-ke: x (x + y) = x² +xy

Isici esivamile

Ukuhlola ama-polynomials akwenzeki ngaso sonke isikhathi. Kuyadingeka ukuthi okungenani kube nento eyodwa ejwayelekile phakathi kwabo. Umqondo ofanayo usebenza lapha njengamanani aphambili, ahlukaniswa kuphela ngabo nangobunye. Ngendlela efanayo, kukhona ama-polynomials ahlukaniswa kuphela yiwo futhi yi-1.

Isibonelo, sinesisho esithi: xa + yb + zc. Njengoba ubona, asikho isici esivamile phakathi kwasos. Kulezi zimo, ukukhishwa kwamafayela akunakwenziwa.

Isici esivamile se-polynomial yi- isihlukanisi esivame kakhulu kulawo magama eyakhiwe ngaso. Lesi yisibonelo salokho:

Enkulumweni a²x + a²futhi into ejwayelekile yi²

Ukwenza i-factorization, hlukanisa amagama nge², Ngakho:

• a²x: a² =x
• a²y: a² = futhi

Ngale ndlela, ukwenziwa kwezinto kubukeka kanjena:

a²x + a²y = kwe²(x + y)

Isici esivamile lapho kufakwa ama-polynomials

Lapho kuhlanganiswa ama-polynomials kunjalo amanye amagama anezici ezifanayo, kanti amanye awanayo. Uma lokhu kwenzeka, okumele kwenziwe ukuqoqwa kwemigomo, kusetshenziswa amabakaki.

Ukuqoqa kungenziwa ngezindlela ezahlukahlukene. Ukuphela kwento ebalulekile ukuthi amagama aqokiwe anento efanayo. Akunandaba ukuthi ukuqoqwa kwenziwa kanjani, umphumela uyohlala ufana. Lesi yisibonelo:

xa + ya + xb + yb

Lawa magama angaqoqwa kanjena:

(xa + ya) + (xb + yb)

Ngemuva kwalokho, bazoba kanjena:

(x + y) + b (x + y)

Ngokukhipha into ejwayelekile nokufaka amafayili, lokhu kungaba umphumela:

uma + ya + xb + yb = (x + y) (a + b)

Njengoba kushiwo ngenhla, ukuqoqa kungenziwa ngezindlela eziningi. Kulesi sibonelo esifanayo, kukhona enye indlela yokuqoqa imigomo:

xa + ya + xb + yb

(xa + xb) + (ya + yb)

x (a + b) + y (a + b)

xa + ya + XB + yb = (a b +) (x + y)

Njengoba kuphawuliwe, umphumela wokugcina uhlala ufana. Umthetho wokushintshana uyagcwaliseka: ukuhleleka kwezinto akukushintshi umkhiqizo.

Ama-factor polynomials ngemikhiqizo emangalisayo

Enye indlela yokufaka ama-polynomials yile ngemikhiqizo emangalisayo, okuyilawa: i-square trinomial ephelele ne-trinomial yefomu x2 + bx + c. Amanye amacala womkhiqizo aphawulekayo ku-algebra asebenza kuphela kuma-binomials.

Isikwele esiphelele trinomial

Es i-polynomial enamagama amathathu, okuwumphumela wokuklama ama-binomial amabili alinganayo. Umthetho uthi: "Noma isiphi isamba samabinomial squared silingana nesikwele sethemu yokuqala, siphindwe kabili izikhathi zokuqala ithemu lesibili, kanye nesikwele sethemu yesibili."

Ngakho-ke, inqubo yokwenza amaphuzu kulokhu kunjalo:

• Thatha impande eyisikwele yetemu lokuqala nelesithathu
• Hlukanisa izimpande ngesibonakaliso esihambelana nethemu yesibili
• Isikwele i-binomial eyakhiwe

Isibonelo:

4 ukuze² - 12ab + 9 b²

• Impande eyisikwele ye-4 a² = 2
• Impande eyisikwele ka-9 b² = 3b

Ngakho:

4 ukuze² - 12ab + 9 b²  = (2 - 3b)²

I-Trinomial yefomu x² + b x + c

Into yokuqala okufanele uyenze qinisekisa ukuthi i-trinomial ihlangabezana nemingcele elandelayo:

• I-coefficient yethemu lokuqala kufanele ibe ngu-1.
• Ithemu yokuqala kufanele ibe yincwadi eyisikwele.
• Ithemu lesibili linenhlamvu efanayo nethemu yokuqala, kepha alilinganiswa ngesikwele, okusho ukuthi, linokucacisa ngo-1.
• I-coefficient yethemu lesibili ingaba yinoma yiliphi inani, kungaba nesibonakaliso esihle noma esibi.
• Ithemu lesithathu alihlangene negama lokuqala, noma negama lesibili. Ngamanye amagama, kungumbuzo wanoma yibuphi ubuningi, ngaphandle kokuhlobana nokwedlule.

Isibonelo sokufaka ama-polynomials

Isibonelo esilandelayo sikhombisa ukuthi kufanele kwenziwe kanjani ama-polynomials ezinesakhiwo:

Faka into ku-trinomial: x² +9x +14

Ukuze wenze lokhu, udinga ukwenza inqubo elandelayo:

• U-trinomial kufanele ukubola kube ngama-binomial amabili.
• Ithemu lokuqala lawo womabili ama-binomial kufanele libe yimpande eyisikwele yethemu lokuqala le-trinomial, okungukuthi: "x".
• I-Los izimpawu zemigomo zimiswe kanjena:
• Uma igama lesibili nelesithathu linophawu oluvumayo, womabili ama-binomials azoba nesibonakaliso esivumayo.
• Uma igama lesibili lingenalo iqiniso futhi igama lesithathu livumelekile, womabili ama-binomials azoba nesibonakaliso esibi.
• Uma igama lesibili lithi u-positive kanti elesithathu alinawo, la magama amabili azoba nezimpawu ezihlukile. Uphawu oluvumayo luzonikezwa kunani elinenani eliphelele kakhulu.
• Ithemu lesibili lama-binomials Kufanele kube yizinombolo ezimbili okuthi, uma zifakwa, zinikeze u-9 (Coefficient wethemu yesibili ye-trinomial) futhi uma iphindaphindwa, unikeze u-14 (inani lethemu lesithathu).

Ngakho-ke, ukwenziwa kwe-trinomial kuthathwe njengesibonelo: x² + 9x + 14, kungabonakala kanjena:

x² + 9x + 14 = (x + 7)(x + 2)

Njengoba kuphawuliwe, igama ngalinye lihambisana nemingcele ebonisiwe:

• "X" impande eyisikwele yethemu lokuqala "x²".
• Njengoba womabili la magama anesibonakaliso esivumayo, ama-binomials amabili anesibonakaliso esihle.
• Amagama wesibili wama-binomials ayanezelwa ku-9 futhi uma ephindaphindwa anika njengomkhiqizo we-14.

Ngabe unemibuzo mayelana nokuthi kanjani izici polynomials?