1)développer : f(x)=36-9(2x-3)²
f(x)= 36-9(2x-3)(2x-3)
f(x)= 36-9(4x²-6x-6x+9)
f(x)= 36-9(4x²-12x+9)
f(x)= 36-36x²+108x-81
f(x)= -36x²+108x-45
2) Factoriser: f(x) =36-9(2x-3)²
f(x)= 6²-9(2x-3)²
f(x)= [6-9(2x-3)][6+9(2x-3)]
f(x)= [6-18x+27)][(6+18x-27)]
f(x)= (-18x+33)(18x-21)
3) calculer:
f(3/2) =36-9[2(3/2)-3]²
f(3/2)= 36-9(3-3)²
f(3/2)= 36
f(0)=36-9(2x-3)²
f(0)= 36
f(1/2)=36-9[2(1/2)-3]²
f(1/2)= 36-9(-2)²
f(1/2)= 36-18
f(1/2)= 18
4) résoudre l'équation suivante: f(x)=-45
-36x²+108x-45=-45
-36x²+108x-45+45=0
-36x²+108x=0
-36x (x-3)=0
-36x=0 ou x-3=0
x=0 x=3 S={0 ; 3}
