Pawg yog cov txheej txheem tshwj xeeb uas siv los ntsuas cov lej sib npaug. Koj tuaj yeem siv nws nrog cov lej sib npaug thiab cov zauv uas muaj plaub nqe lus. Ob txoj hauv kev yuav luag zoo ib yam, tab sis txawv me ntsis.
Kauj ruam
Txoj Kev 1 ntawm 2: Kev Sib Piv Plaub Ntug
Kauj Ruam 1. Saib cov kab zauv
Yog tias koj npaj yuav siv txoj hauv kev no, qhov sib npaug yuav tsum ua raws daim ntawv yooj yim: ax2 bx + c
- Cov txheej txheem no feem ntau yog siv thaum tus coj ua coefficient (lub sijhawm) yog tus lej uas tsis yog "1", tab sis nws kuj tseem tuaj yeem siv rau kev ua zauv sib npaug qhov twg a = 1.
- Ej.: 2 x2 X + 4x + 10
Kauj Ruam 2. Nrhiav cov khoom tseem ceeb ntawm
Muab cov ntsiab lus a thiab c. Cov khoom lag luam ntawm ob nqe lus no yog hu ua cov khoom tseem ceeb.
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Ej.: 2 x2 X + 4x + 10
- ua = 2; c = 10 hli
- ib * c = 2 * 10 = 20
Kauj Ruam 3. Cais cov khoom lag luam rau hauv nws cov khoom ua ke
Sau cov xwm txheej ntawm koj cov khoom lag luam tseem ceeb los ntawm kev cais lawv ua khub ua ke (cov khub xav tau kom tau txais cov khoom tseem ceeb).
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Piv txwv: Qhov tseem ceeb ntawm 20 yog: 1, 2, 4, 5, 10, 20
Sau ua ob peb yam: (1, 20), (2, 10), (4, 5)
Kauj Ruam 4. Nrhiav ib khub ntawm cov lej nrog cov lej sib npaug b
Saib hauv tus lej tus lej thiab txiav txim siab tus khub uas yuav muab lub sij hawm b - lub sij hawm nruab nrab thiab x coefficient - thaum ntxiv ua ke.
- Yog tias koj cov khoom tseem ceeb tsis zoo, koj yuav tsum tau nrhiav ib khub ntawm yam uas sib npaug rau lub sij hawm b thaum rho los ntawm ib leeg.
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Ej.: 2 x2 X + 4x + 10
- b = 9 hli
- 1 + 20 = 21; qhov no tsis yog khub niam txiv txoj cai
- 2 + 10 = 12; qhov no tsis yog khub niam txiv txoj cai
- 4 + 5 = 9; qhov no yog tus khub tseeb
Kauj Ruam 5. Muab lub sij hawm nruab nrab faib ua ob yam
Rov sau dua lub sijhawm nruab nrab los ntawm kev cais nws mus rau hauv cov lej uas tau tshawb nrhiav yav tas los. Xyuas kom koj nkag mus rau qhov kos npe raug (ntxiv lossis rho tawm).
- Nco ntsoov tias qhov kev txiav txim ntawm nqe lus nruab nrab tsis tseem ceeb rau qhov teeb meem no. Tsis muaj teeb meem qhov kev txiav txim ntawm cov lus koj sau, qhov tshwm sim yuav zoo ib yam.
- Ej.: 2 x2 9x + 10 = 2x2 X + 4x + 10
Kauj Ruam 6. Pawg pab pawg los tsim ua khub
Pawg thawj ob nqe lus ua ib khub thiab ob nqe lus thib ob ua ib khub.
Ej.: 2 x2 X 5x + 4x + 5 = 102 (X 5x + 4x + 5)
Kauj Ruam 7. Ntsuas txhua khub
Nrhiav cov xwm txheej sib xws ntawm tus khub thiab cais lawv tawm. Sau qhov sib npaug kom raug.
Piv txwv: x (2x + 5) + 2 (2x + 5)
Kauj Ruam 8. Txheeb tawm qhov sib npaug sib npaug
Yuav tsum muaj cov lej sib thooj ntawm ob qho tib si. Txheeb cov kab zauv no tawm thiab tso lwm cov ntsiab lus hauv lwm cov kab zauv.
Piv txwv: (2x + 5) (x + 2)
Kauj Ruam 9. Sau koj cov lus teb
Tam sim no koj muaj koj cov lus teb.
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Ej.: 2 x2 + 9x + 10 = (2x + 5) (x + 2) (4x + 2)
Cov lus teb zaum kawg yog: (2x + 5) (x + 2) (4x + 5)
Piv txwv ntxiv
Kauj Ruam 1. Yam:
4x ua2 -3x10
- ib * c = 4 * -10 = -40
- Yam 40: (1, 40), (2, 20), (4, 10), (5, 8)
- Qhov tseeb khub ntawm yam: (5, 8); 5 - 8 = -3
- 4x ua2 -8x + 5x - 10
- (4x ib2 -8) + (5x - 10) (Luas)
- 4x (x - 2) + 5 (x - 2)
- (x - 2) (4x + 5)
Kauj Ruam 2. Yam:
8 xto2 + X - - 4x - 3
- ib * c = 8 * -3 = -24
- Qhov tseem ceeb ntawm 24: (1, 24), (2, 12), (4, 6)
- Qhov tseeb khub ntawm yam: (4, 6); 6 - 4 = 2
- 8 xto2 6x + 4x - 3
- (8x ib2 (4x + 3)
- 2 (4x + 3) - 1 (4x + 3)
- (4x + 3) (2x - 1)
Txoj Kev 2 ntawm 2: Cov lej uas muaj plaub Yam Lus
Kauj Ruam 1. Saib cov kab zauv
Qhov sib npaug yuav tsum muaj plaub nqe lus sib cais. Txawm li cas los xij, daim ntawv ntawm plaub pab neeg tuaj yeem sib txawv.
- Feem ntau, koj yuav siv txoj hauv kev no yog tias koj pom cov lej sib npaug uas zoo li: ax3 + xwb2 + txx + d
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Qhov sib npaug kuj tuaj yeem zoo li:
- axy + los + cx + d
- taus2 + bx + cxy + dy
- taus4 + xwb3 + txc2 + dx ua
- Los yog yuav luag tib yam kev hloov pauv.
- Ex: 4x ua4 + 12 x po3 + 6x ib2 + 18x ib
Kauj Ruam 2. Txheeb tawm qhov tseem ceeb tshaj plaws (GCF)
Txiav txim siab yog tias plaub nqe lus muaj ib yam zoo ib yam. Qhov tseem ceeb tshaj plaws ntawm plaub nqe lus, yog ib qho ntawm cov xwm txheej sib xws, yuav tsum tau muab cais tawm ntawm qhov sib npaug.
- Yog tias tsuas yog ib qho plaub nqe lus sib xws yog tus lej "1", tom qab ntawd lub sijhawm ntawd tsis muaj GCF thiab tsis muaj ib yam twg tuaj yeem muab cais tawm ntawm cov kauj ruam no.
- Thaum koj txiav txim siab tawm GCF, nco ntsoov tias koj tseem sau GCF ntawm sab xub ntiag ntawm koj qhov sib npaug thaum koj ua haujlwm. Qhov kev tawm dag zog GCF no yuav tsum suav nrog ib feem ntawm koj cov lus teb kawg rau koj cov lus teb kom raug.
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Ex: 4x ua4 + 12 x po3 + 6x ib2 + 18x ib
- Txhua lub sij hawm sib npaug rau 2x, yog li qhov teeb meem no tuaj yeem rov sau dua li:
- 2x (2x ib3 + 6x ib2 (X 3x+4x+9)
Kauj Ruam 3. Ua pawg me me hauv qhov teeb meem
Pawg thawj ob nqe lus thiab ob nqe lus thib ob.
- Yog thawj lo lus ntawm pab pawg thib ob muaj cov cim rho tawm nyob rau ntawm nws xub ntiag, koj yuav tsum muab cov cim rho tawm tso rau ntawm xub ntiag thib ob. Koj yuav tsum hloov daim paib ntawm lub sijhawm thib ob hauv pab pawg thib ob kom phim nws.
- Piv txwv: 2x (2x3 + 6x ib2 3 (x + + 4x + 9) = 2x3 + 6x ib2(X 3x + 4x + 9)
Kauj Ruam 4. Txheeb tawm GCF los ntawm txhua tus lej
Txheeb xyuas GCF hauv txhua tus lej ob tus lej thiab ua kom GCF nyob sab nraum tus khub. Sau qhov kev ua zauv no kom raug.
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Hauv cov kauj ruam no, koj yuav ntsib nrog kev xaiv ntawm kev cais tawm tus lej zoo lossis tsis zoo rau pawg thib ob. Saib cov cim qhia ua ntej nqe ob thiab thib plaub.
- Thaum ob lub cim zoo ib yam (ob qho zoo lossis ob qho tsis zoo), tawm tus lej zoo.
- Thaum ob lub cim sib txawv (ib qho tsis zoo thiab ib qho zoo), cais tawm tus lej tsis zoo.
- Piv txwv: 2x [(2x3 + 6x ib2) + (3x + 9)] = 2x2[2x ib2(x + 3) + 3 (x + 3)]
Kauj Ruam 5. Txheeb tawm tib lub zauv zauv
Cov zauv ob tog hauv ob kab zauv yuav tsum zoo ib yam. Txheeb xyuas qhov khub no tawm ntawm qhov kev ua zauv, tom qab ntawd faib cov ntsiab lus ntxiv mus rau lwm cov ntawv.
- Yog tias cov lej hauv kab ntawv sib dhos tsis sib xws, rov ua dua koj li haujlwm lossis sim rov kho koj cov lus thiab rov ua qhov sib npaug.
- Txhua kab zauv yuav tsum zoo ib yam. Yog tias lawv tsis zoo ib yam, qhov teeb meem yuav tsis raug txiav txim los ntawm pab pawg lossis lwm txoj hauv kev txawm tias koj sim ua ib txoj hauv kev twg.
- Ej.: 2 x2[2x ib2(x + 3) + 3 (x + 3)] = 2x2[(x + 3) (2x2 + 3)]
Kauj Ruam 6. Sau koj cov lus teb
Koj yuav muaj koj cov lus teb ntawm cov kauj ruam no.
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Ex: 4x ua4 + 12 x po3 + 6x ib2 + 18x = 2 x2(x + 3) (2x2 + 3)
Cov lus teb zaum kawg yog: 2x ua2(x + 3) (2x2 + 3)
Piv txwv ntxiv
Kauj Ruam 1. Yam:
6 x ygo2 + 2xy - 24x - 8y
- 2 [x3x2 +xy - 12x - 4y]
- 2 [(4x2 + xy) - (12x + 4y)]
- 2 [x (3x + y) - 4 (3x + y)]
- 2 [(3x + y) (x - 4)]
- 2 (3x + y) (x - 4)
Kauj Ruam 2. Yam:
x kev3 - 2x ib2 + 4x - 10
- (xwm3 - 2x ib2) + (5x - 10) XV
- x kev2(x - 2) + 5 (x - 2)
- (x - 2) (x2 + 5)
