Bonjour, merci d’avance pour ceux qui m’aideront, bonne journée a vous

bonjour,
f(x)=x²-6x-7
x²-6x=(x²--6x+9)-9
(x-3)²-9
f(x)=(x-3)²-9-7
f(x)=(x-3)²-16

f(x)=(x-3)²-16
f(x)=(x-3)²-4²
f(x)=((x-3)+4))((x-3)-4))
f(x)=(x-3+4)(x-3-4)
f(x)=(x+1)(x-7)

x+1=0 x=-1
x-7=0 x=7

x                  -∞                        -1                     7                     +∞
x+1                             -             0        +                       +
x-7                             -                        -            0          +
(x+1)(x-7)                     +           0       -            0           +

f(x)<0
signe de f(x)=-
f(x)<0 x ∈]-1;7[  ou -1<x<7