1. a. (x-3)² - 25 = x²-6x+9-25 = x²-6x-16 = f(x)
b. (x-3)²-25 = (x-3)²-5² = (x-3+5)(x-3-5) = (x+2)(x-8) = f(x)
2. a) utilisation (3)
f(3) = (3+2)(3-8) = 5*-5 = -25
b) f(x) = 0 utilisation (3)
(x+2)(x-8) = 0
x+2=0 x-8=0
x=-2 x=8
c) f(x)=-16
utilisation (2)
x²-6x-16 = -16
x²-6x = 0
x(x-6) = 0
x=0 x-6=0
x=6
d) f(x)=-25
utilisation (1)
(x-3)²-25=-25
(x-3)² = 0
donc x-3=0
x=3
