Répondre :
[tex]f(x)=(3x+7)^2+(18x+42)+(9x^2-49)\\=9x^2+42x+49+18x+42+9x^2-49\\=18x^2+60x+42\\\\f(x)=(3x+7)^2+(18x+42)+(9x^2-49)\\=(3x+7)^2+6(3x+7)+(3x-7)(3x+7)\\=(3x+7)(3x+7+6+3x-7)\\=(3x+7)(6x+6)\\=6(3x+7)(x+1)\\\\g(x)=x^2+2x+1-(x+1)(2x-7)-(x^2-1)\\=x^2+2x+1-2x^2+7x-2x+7-x^2+1\\=-2x^2+7x+9\\\\g(x)=x^2+2x+1-(x+1)(2x-7)-(x^2-1)\\=(x+1)^2-(x+1)(2x-7)-(x+1)(x-1)\\=(x+1)(x+1-2x+7-x+1)\\=(x+1)(-2x+9)[/tex]
En espérant t'avoir aidé.
En espérant t'avoir aidé.
Bonjour
f(x)=(3x+7)²+(18x+42)+(9x²-49)
f(x) = 9x² +42x +49 + 18x +42 + 9x² -49
f(x) = 18x² +60x +42
Factorisation
f(x) = (3x+7)² + (18x +42) + (3x -7)(3x+7)
(3x+7) (3x+7) + (18x+42 + 3x -7)
(3x+7)(3x+7 + 21x + 35)
(3x+7)(24x +42)
De même pour :
g(x)=x²+2x+1-(x+1)(2x-7)-(x²-1)
g(x) = x² +2x +1 -(2x² -7x +2x -7) - (x² -1)
g(x) = x² +2x +1 -2x² +7x -2x +7 - x² +1
g(x) = -2x² +7x +9
factorisation
g(x) = x²+2x+1-(x+1)(2x-7)-(x²-1)
g(x) = (x +1)² - (x+1) (2x-7) - (x-1)(x+1)
g(x) = (x+1)(x+1) - (2x -7) - (x-1)
g(x) = (x+1)(x+1 -2x +7 -x +1)
g(x) = (x+1)( -2x +9)
f(x)=(3x+7)²+(18x+42)+(9x²-49)
f(x) = 9x² +42x +49 + 18x +42 + 9x² -49
f(x) = 18x² +60x +42
Factorisation
f(x) = (3x+7)² + (18x +42) + (3x -7)(3x+7)
(3x+7) (3x+7) + (18x+42 + 3x -7)
(3x+7)(3x+7 + 21x + 35)
(3x+7)(24x +42)
De même pour :
g(x)=x²+2x+1-(x+1)(2x-7)-(x²-1)
g(x) = x² +2x +1 -(2x² -7x +2x -7) - (x² -1)
g(x) = x² +2x +1 -2x² +7x -2x +7 - x² +1
g(x) = -2x² +7x +9
factorisation
g(x) = x²+2x+1-(x+1)(2x-7)-(x²-1)
g(x) = (x +1)² - (x+1) (2x-7) - (x-1)(x+1)
g(x) = (x+1)(x+1) - (2x -7) - (x-1)
g(x) = (x+1)(x+1 -2x +7 -x +1)
g(x) = (x+1)( -2x +9)