Kev sib piv yooj yim ua rau lawv ua haujlwm tau yooj yim dua, thiab cov txheej txheem yooj yim yog qhov yooj yim heev. Nrhiav qhov loj tshaj plaws ntawm ob tog ntawm qhov sib piv thiab faib tag nrho cov lus qhia los ntawm qhov ntau.
Kauj ruam
Txoj Kev 1 ntawm 3: Txoj Kev Ib: Kev Sib Piv Yooj Yim
Kauj Ruam 1. Saib qhov sib piv
Kev sib piv yog ib qho kev qhia siv los sib piv ob qhov ntau. Kev sib piv yooj yim tuaj yeem ua tam sim ntawd, tab sis yog tias kev sib piv tsis tau yooj yim dua, koj yuav tsum yooj yim tam sim no kom ua qhov ntau kom yooj yim los sib piv thiab nkag siab. Txhawm rau kom yooj yim rau kev sib piv, koj yuav tsum faib ob sab los ntawm tus lej qub.
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Piv txwv:
15:21
Nco ntsoov tias tsis muaj tus lej tseem ceeb hauv qhov piv txwv no. Yog li, koj yuav tsum txheeb xyuas ob tus lej txhawm rau txiav txim siab tias ob nqe lus muaj qhov zoo ib yam lossis tsis yog, uas tuaj yeem siv rau hauv cov txheej txheem yooj yim
Kauj Ruam 2. Txheeb tawm thawj tus lej
Ib qho tseem ceeb yog cov lej sib faib uas faib ib lo lus sib npaug, muab rau koj tag nrho cov lej. Ob nqe lus hauv kev sib piv yuav tsum muaj yam tsawg ib yam sib xws (tsis yog 1). Tab sis ua ntej koj tuaj yeem txiav txim siab yog tias ob nqe lus muaj tib yam xwm txheej, koj yuav tsum nrhiav cov xwm txheej ntawm txhua lub sijhawm.
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Piv txwv:
Tus lej 15 muaj plaub yam tseem ceeb: 1, 3, 5, 15
- 15 / 1 = 15
- 15 / 3 = 5
Kauj Ruam 3. Txheeb tawm tus lej thib ob
Hauv ib qho chaw cais, sau tag nrho cov xwm txheej ntawm lub sijhawm thib ob ntawm kev sib piv. Txog tam sim no, tsis txhob txhawj xeeb txog cov xwm txheej ntawm thawj lub sij hawm thiab tsuas yog tsom mus rau qhov teeb meem thib ob.
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Piv txwv:
Tus lej 21 muaj plaub yam tseem ceeb: 1, 3, 7, 21
- 21 / 1 = 21
- 21 / 3 = 7
Kauj Ruam 4. Nrhiav qhov zoo tshaj plaws
Saib cov xwm txheej hauv ob nqe lus hauv koj qhov kev sib piv. Vajvoog, sau cov npe, lossis txheeb xyuas txhua tus lej uas tshwm hauv ob daim ntawv teev npe. Yog tias qhov sib npaug tsuas yog 1, tom qab ntawd kev sib piv yog hauv nws daim ntawv yooj yim tshaj plaws thiab peb tsis tas yuav ua ib qho haujlwm. Txawm li cas los xij, yog tias ob nqe lus ntawm kev sib piv muaj lwm qhov sib xws, nrhiav qhov zoo thiab txheeb xyuas tus lej loj tshaj plaws. Tus lej no yog koj qhov tseem ceeb tshaj (GCF).
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Piv txwv:
Ob qho 15 thiab 21 muaj ob yam sib xws: 1 thiab 3
GCF rau ob tus lej los ntawm koj qhov kev sib piv thawj zaug yog 3
Kauj Ruam 5. Faib ob tog los ntawm lawv qhov ntau tshaj
Txij li ob nqe lus ntawm koj qhov kev sib piv thawj zaug muaj tib GCF, koj tuaj yeem faib ob tog sib cais thiab tsim ua ib tus lej. Ob tog yuav tsum tau faib los ntawm lawv GCF; tsis txhob faib ib sab.
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Piv txwv:
Ob leeg 15 thiab 21 yuav tsum muab faib ua 3.
- 15 / 3 = 5
- 21 / 3 = 7
Kauj Ruam 6. Sau cov lus teb zaum kawg
Koj yuav tsum muaj cov ntsiab lus tshiab ntawm ob sab ntawm kev sib piv. Koj qhov piv tshiab yog sib npaug rau qhov piv txwv qub, txhais tau tias qhov ntau ntawm ob daim ntawv yog nyob hauv tib qho kev faib ua feem. Tseem nco ntsoov tias qhov ntau ntawm ob sab ntawm koj qhov kev sib piv tshiab yuav tsum tsis muaj tib yam.
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Piv txwv:
5:7
Txoj Kev 2 ntawm 3: Txoj Kev Ob: Kev Sib Piv Algebra Yooj Yim
Kauj Ruam 1. Saib qhov sib piv
Hom kev sib piv no tseem piv ob qhov ntau, tab sis muaj qhov sib txawv ntawm ib lossis ob sab. Koj yuav tsum ua kom yooj yim ob qho lej thiab cov ntsiab lus sib txawv thaum saib rau daim ntawv yooj yim ntawm qhov kev sib piv no.
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Piv txwv:
18x ua2Ib: 72x
Kauj Ruam 2. Txiav tawm ob nqe lus
Nco ntsoov tias yam tseem ceeb yog tus lej uas tuaj yeem faib tus lej sib npaug. Saib cov lej lej ntawm ob sab ntawm kev sib piv. Sau tag nrho cov xwm txheej ntawm ob nqe lus hauv ib daim ntawv cais.
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Piv txwv:
Txhawm rau daws qhov teeb meem no, koj yuav tsum nrhiav yam tseem ceeb ntawm 18 thiab 72.
- Yam tseem ceeb ntawm 18 yog: 1, 2, 3, 6, 9, 18
- Cov xwm txheej ntawm 72 yog: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
Kauj Ruam 3. Nrhiav qhov zoo tshaj plaws
Saib ob daim ntawv teev npe ntawm cov yam tseem ceeb thiab lub voj voog, kos kab hauv qab, lossis txheeb xyuas txhua yam tseem ceeb uas ob daim ntawv teev npe muaj qhov sib xws. Los ntawm qhov kev xaiv tshiab ntawm tus lej, txheeb xyuas tus lej loj tshaj plaws. Tus nqi no yog koj qhov tseem ceeb tshaj plaws (GCF) ntawm cov lus. Txawm li cas los xij, nco ntsoov tias tus nqi no sawv cev tsuas yog ib feem ntawm koj li GCF tiag hauv kev sib piv.
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Piv txwv:
Ob qho 18 thiab 72 muaj ntau yam sib xws: 1, 2, 3, 6, 9, thiab 18. Ntawm tag nrho cov xwm txheej no, 18 yog qhov loj tshaj.
Kauj Ruam 4. Faib ob tog los ntawm lawv qhov ntau tshaj
Koj yuav tsum muaj peev xwm faib faib ob qho tib si hauv koj qhov piv rau GCF. Ua qhov faib tam sim no thiab sau tag nrho cov lej koj tuaj nrog. Cov lej no yuav raug siv hauv koj qhov kev sib piv yooj yim kawg.
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Piv txwv:
Ob qho 18 thiab 72 tau faib los ntawm ib qho ntawm 18.
- 18 / 18 = 1
- 72 / 18 = 4
Kauj Ruam 5. Txheeb tawm qhov hloov pauv, yog ua tau
Saib cov kev hloov pauv ntawm ob sab ntawm kev sib piv. Yog tias tib qhov sib txawv tshwm ntawm ob sab ntawm kev sib piv, tom qab ntawd qhov sib txawv tuaj yeem raug cais tawm.
- Saib ntawm qhov nthuav tawm ntawm qhov sib txawv ntawm ob sab. Lub zog qis yuav tsum tau muab rho tawm los ntawm lub zog loj dua. Nkag siab tias los ntawm kev rho tawm ib lub hwj chim los ntawm lwm qhov, koj yeej ib txwm faib qhov sib txawv loj los ntawm qhov sib txawv me dua.
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Piv txwv:
Thaum kuaj cais, qhov sib txawv ntawm qhov sib piv yog: x2: xwm
- Koj tuaj yeem txiav tawm x los ntawm ob sab. Lub zog ntawm thawj x yog 2, thiab lub zog ntawm x thib ob yog 1. Yog li, ib qho x tuaj yeem raug cais tawm ntawm ob sab. Thawj lub sijhawm yuav nyob nrog ib x thiab lub sijhawm thib ob yuav sab laug yam tsis muaj x.
- x * (x: 1)
- xwm: 1
Kauj Ruam 6. Sau koj qhov tseem ceeb tshaj plaws
Ua ke GCF ntawm koj tus lej suav nrog GCF ntawm koj qhov kev hloov pauv kom pom koj li GCF tseeb. GCF yog lub sijhawm tiag tiag uas yuav tsum tau muab cais tawm ntawm txhua qhov koj sib piv.
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Piv txwv:
Koj qhov tseem ceeb tshaj plaws rau qhov teeb meem no yog 18x.
18x * (x: 4)
Kauj Ruam 7. Sau koj cov lus teb zaum kawg
Thaum koj tau tshem koj li GCF, qhov sib piv uas seem yog daim ntawv yooj yim ntawm koj qhov teeb meem qub. Qhov kev sib piv tshiab no yuav tsum sib npaug rau qhov sib piv qub thiab cov ntsiab lus ntawm ob sab ntawm kev sib piv yuav tsum tsis muaj tib yam.
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Piv txwv:
xwm: 4
Txoj Kev 3 ntawm 3: Txoj Kev Thib Peb: Kev Sib Piv Polynomial
Kauj Ruam 1. Saib qhov sib piv
Kev sib piv polynomial nyuaj dua li lwm hom kev sib piv. Tseem tseem muaj ob qhov sib piv, tab sis qhov tseem ceeb ntawm cov khoom ntawd tsis pom thiab qhov teeb meem yuav siv sijhawm ntev dua los ua kom tiav. Txawm li cas los xij, cov hauv paus ntsiab lus thiab cov kauj ruam tseem zoo ib yam.
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Piv txwv:
(9x ib2 -8x + 15): (x2 + 4x - 10)
Kauj Ruam 2. Faib thawj qhov ntau rau hauv nws cov yam
Koj yuav tsum txiav txim siab tawm polynomial los ntawm thawj qhov ntau. Muaj ntau txoj hauv kev koj tuaj yeem ua tiav cov kauj ruam no, yog li koj yuav tsum siv koj qhov kev paub txog kev ua zauv sib npaug thiab lwm cov lej sib txawv los txiav txim siab txoj hauv kev zoo tshaj plaws los siv lawv.
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Piv txwv:
Txog qhov teeb meem no, koj tuaj yeem siv cov txheej txheem kev sib cais sib cais.
- x kev2 -8x + 15
- Muab cov ntsiab lus a thiab c: 1 * 15 = 15
- Nrhiav ob tus lej uas sib npaug c thaum sib npaug thiab sib npaug rau tus nqi ntawm lo lus b thaum ntxiv: -5, -3 [-5 * -3 = 15; -5 + -3 = -8]
- Hloov ob tus lej no mus rau thawj qhov sib npaug: x2 -5x - 3 + 15
- Qhov tseem ceeb los ntawm pab pawg: (x - 3) * (x - 5)
Kauj Ruam 3. Txheeb cais qhov thib ob rau hauv nws cov yam
Qhov thib ob ntawm kev sib piv yuav tsum tau txhais ua nws yam.
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Piv txwv:
Siv txoj hauv kev twg los xij uas koj xav rhuav tshem qhov kev qhia thib ob rau hauv nws yam:
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x kev2 + 4x - 10
(x - 5) * (x + 2)
Kauj Ruam 4. Hla tawm tib yam
Sib piv ob hom ntawm koj thawj qhov kev qhia tawm. Nco ntsoov tias qhov tseem ceeb hauv qhov kev siv no yog ib qho ntawm kab lus hauv kab lus. Yog tias ib qho ntawm cov xwm txheej hauv kab lus ntawm ob sab ntawm koj qhov kev sib piv sib npaug, tom qab ntawd cov xwm txheej no tuaj yeem hla tawm.
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Piv txwv:
Daim ntawv ntawm kev sib piv qhov tseeb tau sau ua: [(x-3) (x-5)]: [(x-5) (x+2)]
- Cov xwm txheej uas ib txwm muaj ntawm tus lej thiab cov lej yog: (x-5)
- Thaum tsis suav qhov tseem ceeb, qhov piv txwv tuaj yeem sau ua: (x-5)*[(x-3): (x+2)]
Kauj Ruam 5. Sau koj cov lus teb zaum kawg
Qhov sib piv zaum kawg yuav tsum tsis muaj cov ntsiab lus ntxiv xws li yam thiab yuav tsum sib npaug rau qhov pib sib piv.
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Piv txwv:
(x - 3): (x + 2)
