Bonjour,
1) f(x)= x²+4x-5
a. Démontrer que f(x)= (x+2)²-9
On développe :
f(x)= (x+2)²-9= x²+2x+2x+4-9= x²+4x-5
b. Factoriser f:
f(x)= (x+2)²-9
f(x)= (x+2)²-3² est sous forme de a²-b²= (a-b)(a+b)
f(x)= (x+2-3)(x+2+3)
f(x)= (x-1)(x+5)
2) g(x)= 3(x-1)²-12
a. Développer g:
g(x)= 3(x-x-x+1)-12
g(x)= 3(x²-2x+1)-12
g(x)= 3x²-6x+3-12
g(x)= 3x²-6x-9
Factoriser g:
g(x)= 3(x-1)²-12
g(x)= 3[ (x-1)²- 4 ] **** 12= 3x4
g(x)= 3[ (x-1)²- 2² ] ss forme de a²-b²
g(x)= 3(x-1-2)(x-1+2)
g(x)= 3(x-3)(x+1)
3) h(x)= 1/5(x-3)²-5
Développer h:
h(x)= (x²-3x-3x+9)/5 -5
h(x)= (x²-6x+9)/5 -(5*5)/5
h(x)= (x²-6x-16)/5
Factoriser h:
h(x)= (x²-6x-16)/5
h(x)= (x²+2x-8x-16)/5
on cherche à avoir un dénominateur commun:
h(x)= (x(x+2)-8(x+2))/5
on factorise:
h(x)= [ (x+2)(x-8) ] /5.
