Bonjour,
A(x) = (x+2) (-x+1) - 2 (x+2)(x + 2)
A(x) = - x² + x - 2x + 2 - 2(x² + 4x + 4)
A(x) = - x² - x + 2 - 2x² - 8x - 8
A(x) = - 3x² - 9x - 6
2) Factoriser A(x)
A(x) = (x+2) (-x+1) - 2 (x+2)(x + 2)
A(x) = (x + 2)(- x + 1) - (2x + 4)(x + 2)
A(x) = (x + 2)(- x + 1 - 2x - 4)
A(x) = (x + 2)(- 3x - 3)
A(x) = - 3(x + 2)(x + 1)
3) Résoudre A(x) = 0
A(x) = 0
- 3(x + 2)(x + 1) = 0
Un produit est nul si et seulement si un de ses facteurs est nul.
x + 2 = 0 ou x + 1 = 0
x = - 2 ou x = - 1
S = {- 2 ; - 1}
4) Calculer A(0);A(-2):A(2/3)
A(0) = - 3(0 + 2)(0 + 1)
A(0) = - 3 x 2 x 1
A(0) = - 6
A(- 2) = 0 (voir petit 3)
A(2/3) = - 3(2/3 + 2)(2/3 + 1)
A(2/3) = - 3 x 8/3 x 5/3
A (2/3) = - 3 x 40/3
A = - 120/3
A = - 40
