Correction du n° 11

 

              EXERCICE 11  de la feuille des 17 ex    

                                        Développons, réduisons les expressions:

               •  A(x)  = (2 x+3 ) ( x - 1)  - 2 x ( x- 2 )                 Réponse:            A(x)  =    5 x - 3   

                 En effet :

                      A(x)  =  2 x 2 + 3 x - 3 - 2 x  - 2 x2   + 4 x =  2 x2 + 3x - 3 - 2 x - 2 x2 + 4 x  =   5x - 3   

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                • B(x)  = ( - 2 x + 3 )2 - 2 x 3x                             Réponse:        B ( x ) =  - 2 x2 - 12 x + 9           

                     En effet:

                     B ( x ) =  4 x2 + 9 - 12 x  -  6 x2  = - 2 x2 - 12 x + 9

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                 • C(x)  =  ( 2 x + 1 )2   + ( 3 x - 2 ) ( 3 x + 2 )            Réponse:               C( x ) = 13 x2 + 4 x - 3

                      En effet:

                             C( x ) =  4 x2 + 1 + 4 x   +  9 x2 -  4 =  13 x2 + 4 x - 3

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                   • D(x) = - ( - 3 x - 2 )2  + x ( 2 - x ) ( 3 + x )                 Réponse :          D(x) =   - x 3 - 10 x2 - 6 x - 4    

                      En effet:

                             D(x) = - (  3 x + 2 )2  + ( 2 x - x2 ) (3 + x ) = - ( 9 x+ 4 + 12 x ) + 6 x - 3 x2  - x3 + 2 x

                           D(x) = - 9 x2  - 4 - 12 x  + 6 x - 3 x2   - x3 + 2 x = -  x3  - 10  x2 - 6 x - 4

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                 • E(x) =  ( - 3 + 2 x) ( 3 + 2 x)                                   Réponse:       E( x ) = 4 x-  9

                      En effet:

                      E(x) =( 2 x - 3 ) ( 2 x + 3 ) =  4 x2  -  9 

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