Factorization

 guxnKMf bxwaux dI ivDI

do GwqI bhupd ax²+bx+c, a¹0 dy m`D pd nUM ivBwijq krn dI bdlvIN ivDI a Aqy c dy guxnPl dy icMnH qy inrBr krdI hY:-

(1)  jykr a×c Dnwqmk hovy:- jykr a×c dw guxnPl Dnwqmk hovy qwN x dy guxwNk ‘b’ qoN 1 G`t, qoN aultI igxqI lYNdy hoey Aqy iehnwN dy nwl nwl sMiKAw 1 qoN is`DI igxqI Bwv: 1,2,3,……. lYNdy hoey hyT ilKy Anuswr joVy bxwE:-

x dw guxNwk    sMiKAw      guxnPl

(a)    b-1               1              (b-1)×1

(b)    b-2               2              (b-2)×2

(c)    b-3               3              (b-3)×3

(d)    b-4               4              (b-4)×4

       ………        ………        ……….

       ………         ……..        ………..

       ………         ……..         ………..

ies qrwHN loVINdw joVw iehnwN joiVAwN iv`coN ie`k joVw hY[ Bwv ieh ik ijs joVy dw guxnPl a×c dy brwbr hY, auh joVw hI loVINdw joVw hY[pRwpq joVy iv`c dovyN sMiKAwvwN dy icMnH ‘b’ dy icMnH dy smwn hoxgy[

                              

audwhrn:-

               

            a                            b                                 c
   pihlw pd                 m`D pd                  AKIrlw pd

ie`Qy a×c dw guxnPl=2×6=12 (Dnwqmk) hY[m`D pd -7x iv`c ‘b’ dw guxwNk -7 hY[AsIN ‘b’ dy guxwNk 7 qoN ie`k G`t 6 qoN aultI igxqI ilKdy hoey Aqy dUsry pwsy sMiKAw iv`c ie`k qoN is`DI igxqI ilKdy hoey joVy bxwvwNgy[

x dw guxwNk    sMiKAw     guxnPl

     6      ×     1       =    6

     5      ×     2       =   10

 

 

ies iv`c qIjy joVy dw guxnPl 12 hY jo ik (a×c) dy guxnPl dy brwbr hY[ies leI ieh loVINdw joVw hY Aqy ies dI hryk sMiKAw dw icMnH m`D pd dy icMnH (irxwqmk) dy smwn hovygw[ Bwv ieh ik ieh sMiKAwvwN -4 Aqy -3 hoxgIAwN ijhnwN nUM joV ky m`D pd dw guxwNk -7 bxdw hY Aqy guxnPl 12 bxdw hY[

      ies qrwNH h`l :- 2x²-7x+6

                           = 2x²-4x-3x+6

                           =  2x(x-2)-3(x-2)

                           =  (x-2) (2x-3)

AiBAws leI pRSn

(1)    x²-4x+3

(2)   x²+6x+8

(3)  y²+3y+2