Bonsoir,
A(x)= (x+1)²-(3x+2)(x+1)
1) Développer A(x):
A(x)= x²+2x+1-(3x²+2x+3x+2) changement de signes après suppression de la ( )
A(x)= x²+2x+1-3x²-5x-2
A(x)= -2x²-3x-1
2) Factoriser A(x):
A(x)= (x+1)²-(3x+2)(x+1)
A'x)= (x+1)(x+1-3x-2)
A(x)= (x+1)(-2x-1)
A(x)= -(x+1)(2x+1)
Tableau de signes:
x+1= 0 => x= -1
-2x-1= 0 => -2x= 1 => x= -1/2
x -∞ -1 -1 /2 +∞
x+1 - 0 + +
-2x-1 + + 0 -
P - 0 + 0 -
A(x) < 0 , S= ] -∞ ; -1 [ U ] -1/2 ; +∞ [
