The document contains a math exam with multiple questions regarding polynomials, including: factoring polynomials, solving polynomial equations, performing operations with polynomials, simplifying polynomial expressions, and solving systems of equations. The exam also provides notes indicating it cannot be completed with pens, highlighters, or exchanging materials.

1. džĂŵĞŶ ĚĞ ƌĞĐƵƉĞƌĂĐŝſŶ ĚĞů ϮǑ ƚƌŝŵĞƐƚƌĞ ϰǑ ^K ŽƉĐ͘ ĞƉĂƌƚĂŵĞŶƚŽ ĚĞ DĂƚĞŵĄƚŝĐĂƐ
/͘ ͘^͘ ,ƵĞƌƚĂ ZŽƐĂƌŝŽ
EŽŵďƌĞ LJ ĂƉĞůůŝĚŽƐ͗ͺͺͺͺͺͺͺͺͺͺͺͺͺͺͺͺͺͺͺͺͺͺͺͺͺͺͺͺͺͺͺͺͺͺͺͺͺͺͺͺ ƵƌƐŽ͗ͺͺͺͺͺͺ &ĞĐŚĂ͗ͺͺͺͺͺͺͺ ŶǑ ĚĞ ĨŽůŝŽƐ͗ͺͺͺͺ
'DGR HO PRQRPLR Ȃ ‫ ݔ‬ଵଶ
H &DOFXOD VX YDORU QXPpULFR FXDQGR ‫ ݔ‬ൌ ͳ
D 'L FXiO HV VX SDUWH OLWHUDO E ¢&XiO HV VX FRHILFLHQWH" F ¢&XiO HV VX JUDGR"
G 'D XQ PRQRPLR VHPHMDQWH
D ͷ‫ ݔ‬ହ െ ͵‫ ݔ‬ହ ൅ Ͷ‫ ݔ‬ହ ൅ ͹‫ ݔ‬ହ െ ͳͳ‫ ݔ‬ହ ൅ ‫ ݔ‬ହ E ͹‫ ݔ‬െ ͺ‫ ݔ‬ଶ F ሺ͵‫ ݔ‬ଶ ሻ ȉ ሺͷ‫ݕݔ‬ሻ G ሺ͵‫ ݕݔ‬ଶ ሻଶ ǣ ሺ‫ ݔ‬ଶ ‫ ଺ ݕ‬ሻ
5HDOL]D ODV VLJXLHQWHV RSHUDFLRQHV FRQ PRQRPLRV
'DGR HO SROLQRPLR ܲሺ‫ݔ‬ሻ ൌ ͷ‫ ݔ‬ଶ ൅ Ͷ‫ ݔ‬ସ െ Ͷ െ ʹ‫ ݔ‬ଶ െ ͵‫ ݔ‬ସ ൅ ͳ
D 5HG~FHOR E 'L FXiO HV HO WpUPLQR LQGHSHQGLHQWH F ¢&XiO HV VX JUDGR" G &DOFXOD ܲሺͲሻ
'DGRV ܲሺ‫ݔ‬ሻ ൌ ‫ ݔ‬ସ െ ͵‫ ݔ‬ଷ ൅ ͷ‫ ݔ‬൅ ͵ ô ܳሺ‫ݔ‬ሻ ൌ ʹ‫ ݔ‬ସ ൅ ͸ FDOFXOD ܲሺ‫ݔ‬ሻ െ ܳሺ‫ݔ‬ሻ
ଶ௫ య ି଻௫ మ ିଵଵ௫ାଵଷ
5HDOL]D OD VLJXLHQWH GLYLVLyQ FRPSUXHED UHDOL]DQGR ODV RSHUDFLRQHV QHFHVDULDV TXH HVWi ELHQ
ଶ௫ାଷ
UHVXHOWD
6DFD IDFWRU FRP~Q HO Pi[LPR SRVLEOH HQ OD VLJXLHQWH H[SUHVLyQ ͵‫ ݔ‬ଵଶ െ ͸‫ ݔ‬ଵହ
ሺʹ‫ ݕݔ‬ଶ െ ͵‫ ݔ‬ଶ ሻଶ
ଵ
D 'HVDUUROOD OD VLJXLHQWH H[SUHVLyQ XWLOL]DQGR ODV LGHQWLGDGHV QRWDEOHV
‫ݔ‬ଶ െ
ଵ଺
E ([SUHVD HO VLJXLHQWH SROLQRPLR FRPR SURGXFWR GH GRV IDFWRUHV
െ
ଶ௫ିଷ ௫ାଷ ௫ିଵ
൅Ͷ ൅
ଶ ସ ଶ
6LPSOLILFD
െ ൅
௫ሺ௫ାଷሻ ሺ௫ାଵሻమ ଵ
ଶ ଷ ଷ
6LPSOLILFD
൅ ൅
ଵ ଵ ଵ
௫ିଵ ௫ାଵ ௫ మ ିଵ
6LPSOLILFD
(QFXHQWUD XQD VROXFLyQ DSUR[LPDGD FRQ XQ GHFLPDO GH ‫ ݔ‬ସ ൌ ͷͲͲͲ QR YDOH FDOFXODU GLUHFWDPHQWH
OD UDt] FXDUWD GHO QXPHUR HQ FXHVWLyQ FRQ OD FDOFXODGRUD
5HVXHOYH ODV VLJXLHQWHV HFXDFLRQHV
͵ሺ‫ ݔ‬െ ʹሻ ൅ ͷሺ‫ ݔ‬െ ͳሻ ൌ ʹ‫ ݔ‬െ ʹሺ‫ ݔ‬൅ ͵ሻ ൅ ͳͳ
௫ାଵ ௫ିଷ ௫ି଼
൅ െʹ‫ ݔ‬ൌ െ͸
ଶ ହ ହ
‫ݔ‬ሺʹ െ ‫ݔ‬ሻሺ‫ ݔ‬െ ͹ሻሺ‫ ݔ‬ଶ െ ͻሻ ൌ Ͳ
‫ ݔ‬െ ξ‫ ݔ‬ൌ ʹ
ଵ ଷି௫
െʹ ൌ
௫మ ଷ௫ మ
(QFXHQWUD OD VROXFLyQ R VROXFLRQHV GH ORV VLJXLHQWHV SUREOHPDV FRPSUXHED TXH VRQ ODV YHUGDGHUDV
&DOFXOD OD HGDG GH $OEHUWR VDELHQGR TXH GHQWUR GH DxRV WHQGUi HO WULSOH GH VX HGDG DFWXDO
(O SURGXFWR GH GRV Q~PHURV FRQVHFXWLYRV HV ¢4Xp Q~PHURV VRQ"

2. 5HVXHOYH ORV VLJXLHQWHV VLVWHPDV
Ͷ‫ ݔ‬െ ͷ‫ ݕ‬ൌ െʹ
൜
͵‫ ݔ‬൅ ʹ‫ ݕ‬ൌ ͳͲ
SRU HO PpWRGR GH VXVWLWXFLyQ
͸‫ ݔ‬൅ ʹ‫ ݕ‬ൌ Ͷ
൜
͵‫ ݔ‬൅ ‫ ݕ‬ൌ ʹ
SRU HO PpWRGR GH LJXDODFLyQ
ͷ‫ ݔ‬െ ͵‫ ݕ‬ൌ ͳ
൜
Ͷ‫ ݔ‬൅ ʹ‫ ݕ‬ൌ ͳͶ
SRU HO PpWRGR GH UHGXFFLyQ
&ODVLILFD HO VLJXLHQWH VLVWHPD HQ FRPSDWLEOH H LQFRPSDWLEOH HQ FDVR GH VHU FRPSDWLEOH HQ
GHWHUPLQDGR R LQGHWHUPLQDGR MXVWLILFDQGR OD UHVSXHVWD ¢&XiO HV OD SRVLFLyQ GH ODV UHFWDV TXH OR
‫ݔ‬൅‫ ݕ‬ൌʹ
IRUPDQ"
൜
ʹ‫ ݔ‬൅ ʹ‫ ݕ‬ൌ ͵
5HVXHOYH HO VLJXLHQWH VLVWHPD SRU HO PpWRGR TXH SUHILHUDV
‫ݕ‬െͶ
‫ݔ‬ൌ ൅ͳ
൞ ͵
ͳ ‫ݔ‬൅Ͷ
‫ݕ‬൅ ൌ
͵ ͵
5HVXHOYH HO VLJXLHQWH VLVWHPD SRU HO PpWRGR TXH SUHILHUDV
ʹ‫ ݕݔ‬ൌ ͵
൜
‫ ݔ‬൅ ʹ‫ ݕ‬ൌ Ͷ
1RWDV
• 1R VH SXHGH XVDU QL OiSL] QL EROtJUDIR URMR QL WtSH[ (O XVR GH FXDOTXLHUD GH HOORV DQXODUi OD
SUHJXQWD GRQGH DSDUH]FDQ
• +DEODU DQWHV GH TXH WRTXH HO WLPEUH VXSRQGUi XQ VXVSHQVR LQPHGLDWR GHO H[DPHQ
• 1R VH SXHGH LQWHUFDPELDU PDWHULDO (O KDFHUOR VXSRQGUi XQ VXVSHQVR LQPHGLDWR GHO H[DPHQ
• 7RGDV ODV SUHJXQWDV WLHQHQ HO PLVPR YDORU
3UHJXQWDV D UHDOL]DU
7 7 7
7 7 7 7
7 7 7RGR