On considere l'expression A) = (x - 3)(2x + 1) - (x - 3)(5x - 2). 1. Développer A(x) 2. Factoriser A(x) 3. Calculer A(0) et A(-3)

1.

[tex] A(x) = ( {2x}^{2} + x - 6x - 3) - ({5x}^{2} - 2x - 15x + 6) [/tex]

[tex] A(x) = {2x}^{2} + x - 6x - 3 - {5x}^{2} + 2x + 15 - 6[/tex]

[tex] A(x) = {-3x}^{2} -3x + 6[/tex]

2.

[tex] A(x) = (x - 3)((2x + 1) - (5x - 2))[/tex]

[tex] A(x) = (x - 3)(2x + 1 - 5x + 2)[/tex]

[tex] A(x) = ( x - 3)( - 3x + 3)[/tex]

3. On prend la forme factorisé :

[tex] A(0) = (0 - 3)( - 3 \times 0 + 3) \\ A(0) = - 3 + 3 \\ A(0) = 0[/tex]

[tex] A(-3) = ( - 3 - 3)( - 3( - 3) + 3) \\ A(-3) = - 9 + 9 \\ A(-3) = 0[/tex]