Zinthu polynomials

Kusintha ma polynomials okhala ndi chinthu chofanana

Kulingalira mawu a algebraic ndi njira yomwe, mawu awa alembedwa ngati kuchulukitsa. Polemba zolemba za polynomials zomwe cholinga chake ndi pezani zinthu ziwiri kapena zingapo zomwe ndizofanana ndi algebraic ngati malonda.

Cholinga cholemba ma polynomials ndikuti athe kuyimira polynomial ngati zopangidwa ndi ma polynomial ena angapo ocheperako.

ndi Zomwe zimafotokozera za algebraic ndizofanana kapena zomwe zimafanana. Chofunikira ndikuti akachulukana wina ndi mnzake amapereka zotsatira zomwe ndizofanana ndi chiwonetsero choyamba. Izi zitha kuwonedwa muchitsanzo:

Mawu a algebraic: x (x + y)

Mwa kuchulukitsa mawu wina ndi mnzake, tili ndi: x2 + xy

Chifukwa chake: x (x + y) = x2 + xy

Zomwe zimafala

Kusintha ma polynomials sikotheka nthawi zonse. Amayenera kuti pakhale chinthu chimodzi chofanana pakati pawo. Malingaliro omwewo amagwiranso ntchito pano monga manambala oyamba, omwe amangogawika mwa iwo okha komanso mogwirizana. Momwemonso, pali ma polynomials omwe amangogawana okha ndi 1.

Mwachitsanzo, tili ndi mawu akuti: xa + yb + zc. Monga mukuwonera, palibe chofanana pakati pawos. Pazinthu izi, kulembetsa sikungachitike.

Zomwe zimachitika polynomial ndi chopatulira chachikulu chodziwika kwambiri cha mawu omwe amapangidwa. Ichi ndi chitsanzo cha izi:

M'mawu ake a2x + ndi2ndipo chinthu chofala ndi a2

Kuti muchite izi, gawani mawuwo ndi a2, Kotero:

  • a2x: a2 =x
  • a2y: a2 = ndi

Mwanjira iyi, factorization ikuwoneka motere:

a2x + ndi2y = ndi2(x + y)

Zomwe zimafala polemba ma polynomials

Polemba ma polynomials, ndiye kuti ena mwa mawuwa amakhala ndi chinthu chofanana, pomwe ena alibe. Izi zikachitika, chomwe chiyenera kuchitidwa ndi gulu la mawuwo, pogwiritsa ntchito zolembera.

Kugawa kungachitike m'njira zosiyanasiyana. Chokhacho chofunikira ndikuti mawu omwe ali mgululi amakhala ndi gawo limodzi. Ziribe kanthu momwe gululi lachitika, zotsatira zake sizikhala zofanana. Ichi ndi chitsanzo:

xa + ya + xb + yb

Mawu awa atha kugawidwa motere:

(xa + ya) + (xb + yb)

Ndiye, adzakhala motere:

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

Potenga zomwe zimafala ndikulemba, izi ndi zomwe zidzachitike:

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

Monga tafotokozera pamwambapa, gulu lingachitike m'njira zingapo. Mu chitsanzo chomwechi, alipo njira ina yophatikizira mawuwo:

xa + ya + xb + yb

(xa + xb) + (ya + yb)

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

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

Monga taonera, zotsatira zomaliza nthawi zonse zimakhala zofanana. Lamulo lakusintha lakwaniritsidwa: dongosolo lazinthu silisintha malonda.

Factor polynomials ndi zinthu zodabwitsa

Njira ina yopangira polynomials ndi kudzera muzinthu zodabwitsa, zomwe ndi: trinomial yabwino kwambiri komanso mawonekedwe atatu x2 + bx + c. Milandu ina yodziwika bwino yomwe algebra amawona imagwira ntchito kuma binomials okha.

Malo angwiro okwanira atatu

Es polynomial wopangidwa ndi mawu atatu, zomwe ndi zotsatira zakuyanika ma binomial awiri ofanana. Lamuloli likuti: "Chiwerengero chilichonse cha mabinomial squared chimakhala chofanana ndi bwalo la teremu yoyamba, kuphatikiza kawiri nthawi yoyamba nthawi yachiwiri, kuphatikiza bwalo lachiwiri."

Choncho, ndondomeko yolemba pamenepa ndi:

  • Tengani mizu yaying'ono ya woyamba ndi wachitatu mawu
  • Patulani mizu ndi chikwangwani chomwe chikufanana ndi nthawi yachiwiri
  • Tsamba lalikulu lomwe limapangidwa

Chitsanzo:

4 kuti2 - 12ab + 9 b2

  • Mizu yaying'ono ya 4 a2 = 2a pa
  • Mzu wa Square 9 b2 = 3b ndi

Chifukwa chake:

4 kuti2 - 12ab + 9 b2  = (2 - 3b)2

Zachilendo za mawonekedwe x2 + b x + c

Chinthu choyamba kuchita ndi onetsetsani kuti trinomial ikukwaniritsa izi:

  • Coefficient ya nthawi yoyamba iyenera kukhala 1.
  • Nthawi yoyamba iyenera kukhala kalata yomwe ili ndi mbali ziwiri.
  • Teremu yachiwiri ili ndi chilembo chofanana ndi nthawi yoyamba, koma siyopendekera, ndiye kuti ili ndi chiwonetsero cha 1.
  • Coefficient ya nthawi yachiwiri ikhoza kukhala kuchuluka kulikonse, kaya ndi chizindikiro chabwino kapena cholakwika.
  • Nthawi yachitatu ilibe chochita ndi woyamba, kapena nthawi yachiwiri. Mwanjira ina, ndi funso la kuchuluka kulikonse, popanda ubale uliwonse ndi zam'mbuyomu.

Chitsanzo cha zolemba polynomials

Chitsanzo cha zolemba polynomials

Chitsanzo chotsatira chikuwonetsa fayilo ya momwe ma polynomials ayenera kukhazikitsidwa omwe ali ndi dongosolo ili:

Zinthu zazikuluzikulu: x2 + 9x +14 pa

Kuti muchite izi, muyenera kuchita izi:

  • Atatu ayenera kutero kuvunda mu binomials awiri.
  • Nthawi yoyamba yama binomials onse ayenera kukhala mizu yaying'ono ya nthawi yoyamba ya trinomial, yomwe ndi: "x".
  • ndi zizindikiro za mawuwa akhazikitsidwa motere:
  • Ngati nthawi yachiwiri ndi yachitatu ili ndi chizindikiro chotsimikizika, onse awiri amakhala ndi chizindikiro chotsimikizika.
  • Ngati nthawi yachiwiri ili yolakwika ndipo nthawi yachitatu ili yabwino, ma binomial onse adzakhala ndi chizindikiro cholakwika.
  • Ngati nthawi yachiwiri ili yoyenera ndipo yachitatu ilibe, mawu onsewa adzakhala ndi zizindikilo zosiyana. Chizindikiro chenicheni chidzaperekedwa ku nambala yomwe ili ndi mtengo wapamwamba kwambiri.
  • Nthawi yachiwiri yamankhwalawa Ayenera kukhala manambala awiri omwe, akawonjezeredwa, amapereka 9 (coefficient ya teremu yachiwiri ya trinomial) ndipo akachulukitsidwa, perekani 14 (kuchuluka kwa gawo lachitatu).

Chifukwa chake, kufalikira kwa utatu kumatengedwa monga chitsanzo: x2 + 9x + 14, zitha kuwoneka motere:

x2 + 9x + 14 = (x + 7) (x + 2)

Monga taonera, nthawi iliyonse imagwirizana ndi magawo omwe awonetsedwa:

  • "X" ndiye mizu yayikulu yayikulu "x2".
  • Popeza mawu onsewa ali ndi chizindikiro chotsimikizika, ma binomial awiriwa ali ndi chizindikiro chotsimikizika.
  • Nthawi yachiwiri yama binomial imawonjezerana 9 ndipo ikachulukitsidwa amapereka monga 14.

Kodi muli ndi mafunso aliwonse okhudza momwe mungakhalire chinthu polynomials?


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