bjr
A(x) = 2[(x + 1/24)²- 289/576]
289 = 17²
576 = 24²
289/576 = (17/24)²
A(x) = 2[(x + 1/24)²- (17/24)²] différence de deux carrés
A(x) = 2(x + 1/24 + 17/24)(x + 1/24 - 17/24)
A(x) = 2( x + 18/24)(x - 16/24) (on simplifie 18/24 et 16/24)
A(x) = 2(x + 3/4)(x - 2/3) on développe
A(x) = 2[x² - (2/3)x + (3/4)x - 1/2]
calcul de (-2/3)x + (3/4)x
(-2/3)x + (3/4)x = (-8/12)x + (9/12)x = (1/12)x
on remplace dans A
A(x) = 2[x² + (1/12)x - 1/2] (on distribue 2 sur les termes entre [ ] )
A(x) = 2x² + 2(1/12)x - 2(1/2)
A(x) = 2x² + (1/6)x - 1