Bonjour,
1) Développer:
A(x)= (8x-40)(-5x+12)-(8x-40)²
A(x)= -40x²+200x+96x-480- (64x²-320x-320x+1 600)
A(x)= -40x²+200x+96x-480- (64x²-640x+1 600)
A(x)= -40x²+296x-480-64x²+640x-1 600
A(x)= -104x²+936x-2 080
2) Factoriser:
A(x)= (8x-40)(-5x+12)-(8x-40)²
A(x)= (8x-40)(-5x+12-8x+40)
A(x)= (8x-40)(-13x+52)
A(x)= - (8x-40)(13x-52) ****** (8x-40)= 8(x-5) et (13x-52)= 13(x-4)
A(x)= -8*13( x-5)(x-4)
A(x)= -104 ( x-5)(x-4)
Résoudre A(x)= 0
-104 ( x-5)(x-4)=
x-5= 0 ou x-4= 0
x= 5 x= 4
S= { 4 ; 5 }
