Inqaku polynomials

Ubungakanani benkcazo ye-algebraic yinkqubo apho, eli binzana libhalwe njengokuphindaphinda. Xa kugcinwa iipolynomials into ekujongwe ukuba yenzeke fumana izinto ezimbini okanye ezingaphezulu ezinegama elifanayo le-algebra njengemveliso.

Injongo yokufaka i-polynomials kukukwazi ukumela polynomial njenge Imveliso yezinye iipolynomials ezincinci.

Los Imiba yokubonisa kwe-algebra yimigaqo okanye izinto ezifanayo. Into ebalulekileyo kukuba xa uphinda-phinda kunye nabanye banike isiphumo esilingana nentetho yokuqala. Oku kunokubonwa kumzekelo:

Inkcazo yeAlgebra: x (x + y)

Ngokuphindaphinda amagama kunye nomnye, sine: x² +xy

Ngaloo ndlela: x (x + y) = x² +xy

Into eqhelekileyo

Iifactyn polialomials akusoloko kunokwenzeka. Kuyafuneka ukuba kubekho into ibe nye phakathi kwabo. Ingqondo efanayo isebenza apha njengamanani aphambili, ahluleke ngokwawo nangomanyano. Ngendlela enye, Kukho iipolynomials ezahlula ngokwazo kwaye zi-1.

Umzekelo, sinentetho: xa + yb + zc. Njengokuba ubona, akukho nto ixhaphakileyo phakathi kwayos. Kule meko, ukuhanjiswa kwezinto akunakwenziwa.

Into eqhelekileyo ye-polynomial yile oyena mhlukanisi uqhelekileyo kulawo magama ayilwa ngawo. Lo ngumzekelo woku:

Kwintetho a²x + a²kwaye into eqhelekileyo ngu²

Ukwenza i-factorization, yahlula-hlula ngokwe-a², Ke:

• a²x: a² =x
• a²y: a² = Kunye

Ngale ndlela, i-factorization ijongeka ngoluhlobo:

a²x + a²y = uya²(x + y)

Inqaku eliqhelekileyo xa ubhala iipolynomials

Xa ubeka i-polynomials kwimeko apho amanye amagama anento efanayo, ngelixa amanye engenayo. Xa oku kusenzeka, into ekufuneka yenziwe kukwenziwa iqela lemigaqo, kusetyenziswa abazali.

Ukwahlulahlula amaqela kunokwenziwa ngeendlela ezahlukeneyo. Into ebaluleke kuphela kukuba amagama aqokelelweyo anento efanayo. Nokuba iqela lenziwa njani, iziphumo ziya kuhlala zifana. Lo ngumzekelo:

xa + ya + xb + yb

La magama angaqokelelwa ngolu hlobo:

(xa + ya) + (xb + yb)

Ke baya kuba ngoluhlobo:

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

Ngokukhupha into eqhelekileyo kunye nokwenza ucoceko, oku kunokuba sisiphumo:

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

Njengoko sele kukhankanyiwe apha ngasentla, ukwenza amaqela kunokwenziwa ngeendlela ezininzi. Kulo mzekelo mnye, zikhona enye indlela yokwenza amaqela ngokwemigaqo:

xa + ya + xb + yb

(xa + xb) + (ya + yb)

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

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

Njengoko kubonisiwe, Isiphumo sokuhlala sihlala sinye. Umthetho wokushintshana uzalisekisiwe: ucwangco lwezinto aluguquli imveliso.

Iifactory polynomials ziimveliso ezimangalisayo

Enye indlela yokujonga iipolynomials yile ngeemveliso ezibalaseleyo, eziyi: isikwere esigqibeleleyo seetrinomial kunye netrinomial yefom x2 + bx + c. Amanye amatyala emveliso abalulekileyo kwi-algebra asebenza kuphela kwii-binomials.

Isikwere esigqibeleleyo se-trinomial

Es ipolynomial enamagama amathathu, esisiphumo sokuphamba kabini iibinomials ezilinganayo. Umthetho uthi: "Nasiphi na isixa semigqomo esineebinomials silingana nesikwere sekota yokuqala, dibanisa kabini amaxesha okuqala kwikota yesibini, kunye nesikwere sekota yesibini."

Ngoko ke, Inkqubo yokufaka izinto kule meko yile:

• Thatha ingcambu yesikwere yekota yokuqala neyesithathu
• Yahlula iingcambu ngophawu oluhambelana nekota yesibini
• Isikwere sebinomial eyenziweyo

Umzekelo:

4 a² - 12ab + 9 b²

• Ingcambu yesikwere se-4 a² = 2nd
• Ingcambu yesikwere se-9 b² = 3b

Ngaloo ndlela:

4 a² - 12ab + 9 b²  = (2 - 3b)²

I-Trinomial yefom x² + b x + c

Into yokuqala yokwenza kukuba Qinisekisa ukuba i-trinomial ihlangabezana nezi paramitha zilandelayo:

• Umlingani wekota yokuqala kufuneka abe ngu-1.
• Ikota yokuqala kufuneka ibe yileta ephindwe kabini.
• Ikota yesibini inonobumba ofanayo nekota yokuqala, kodwa ayikwerekwere, oko kukuthi, inombono we-1.
• Umlingani wekota yesibini unokuba nabuphi na ubungakanani, nokuba kungophawu oluchazayo okanye olubi.
• Ixesha lesithathu alinanto yakwenza neyokuqala, okanye neyesibini. Ngamanye amagama, ngumbuzo wabo nabuphi na ubungakanani, ngaphandle kobudlelwane nakwezangaphambili.

Umzekelo wokufaka i-polynomials

Lo mzekelo ulandelayo ubonakalisa indlela polynomials ekufuneka yenziwe ngayo ezinolu lwakhiwo:

Inqaku le-trinomial: x² +9x +14

Ukwenza oku, kuya kufuneka wenze le nkqubo ilandelayo:

• U-trinomial kufuneka ukubola kubini binomial.
• Ikota yokuqala yazo zombini ezi binomials kufuneka ibe yingcambu yesikwere sekota yokuqala ye-trinomial, oko kukuthi: "x".
• Los imiqondiso yemigaqo zimiselwe ngoluhlobo:
• Ukuba ikota yesibini kunye neyesithathu zinophawu oluqinisekileyo, zombini ii-binomials ziya kuba nomqondiso oqinisekileyo.
• Ukuba ikota yesibini ayichanekanga kwaye ikota yesithathu ilungile, zombini iibinomials ziya kuba nophawu olubi.
• Ukuba ikota yesibini inethemba kwaye eyesithathu ayinayo, la magama mabini aya kuba neempawu ezahlukileyo. Uphawu oluqinisekileyo luya kunikwa inani elinelona xabiso liphezulu.
• Ixesha lesibini leebinomials Kufuneka babe ngamanani amabini xa edityanisiweyo anika u-9 (umlingani wekota yesibini ye-trinomial) kwaye xa uphinda-phindwa unike u-14 (isixa sekota yesithathu).

Ngale ndlela, ubungakanani be-trinomial ethathwe njengomzekelo: x² + 9x + 14, inokubonakala ngoluhlobo:

x² + 9x + 14 = (x + 7)(x + 2)

Njengoko kubonisiwe, Ikota nganye ihlangabezana neparamitha ezibonisiweyo:

• "X" yingcambu yekota yokuqala "x²".
• Kuba omabini la magama anesibonakaliso esivumayo, ezi zinto zimbini zineempawu ezintle.
• Imigaqo yesibini yeebinomials yongeza enye kwi-9 kwaye xa iphindaphindwe banika njengemveliso 14.

Ngaba unayo nayiphi na imibuzo malunga nendlela factor polynomials?