Factorisé, développer

F (x) = x(x+2)-(2x-1)(x+2) g(x) = (2x+3)² - (x+1)² 1. Développer f(x) et g(x) f (x) = x(x+2)-(2x-1)(x+2) f (x) = x²+2x-2x²-4x+x+2 f (x) = -x²-x+2 g(x) = (2x+3)² - (x+1)² g(x) = 4x²+12x+9-x²-2x-1 g(x) = 2x²+10x+8 2. Factoriser f(x) et g(x) f(x) = x(x+2)-(2x-1)(x+2) f(x) = (x+2) (x-(2x-1)) f(x) = (x+2) (-2x²+x) f(x) = x (x+2) (-2x+1) g(x) = (2x+3)² - (x+1)² g(x) = [(2x+3) - (x+1)] [(2x+3) + (x+1)] g(x) = (x-2) (3x+4) 3. Calculer f(racine carré de 3)(rac3) et g (racine carré de 5)(rac5) f (x) = -x²-x+2 f (rac3) = -3 -rac3 +2 f (rac3) = -(1+rac3) g(x) = 2x²+10x+8 g(rac5) = 10rac5 + 18 4 Résoudre dans R ( réel ) les equations suivante : a. f(x) = 2 f (x) = -x²-x+2 -x²-x+2 = 2 x(x+1) = 0 S={0;-1} b. g(x) = 0 g(x) = 2x²+10x+8 2x²+10x+8 = 0 c. f(x) = g(x) -x²-x+2 = 2x²+10x+8 -3x²-11x-6 = 0 3x² +11x +6 =0 delta = 121 - 72 = 49 Solution1: (-11-7)/6 = -3 ((-b-racdelta)/2a) Solution2: (-11+7)/6 = -2/3 ((-b-racdelta)/2a) 5. Résoudre dans R (réel) les inéquations suivante : a. g(x) < 8 b. f(x) (>ou =) 0 a. g(x) = 2x²+10x+8 2x²+10x+8 < 8 2x²+10x < 0 x² + 5x < 0 S=]-5;0] b. -x²-x+2 (>ou =) 0 x(x+1) (<ou=) 2 S= [-1;1]