bonjour
a)
P(x) =(x² - 9) - (x - 3)² =
x² - 9 est une différence de 2 carrés
x² - 3² = (x - 3)(x + 3)
(x - 3)² = (x - 3)(x - 3)
P(x) = (x² - 9) - (x - 3)² = (x - 3)(x + 3) - (x - 3)(x - 3)
facteur commun (x - 3)
= (x - 3)(x + 3) - (x - 3)(x - 3)
= (x - 3) [(x + 3) -(x - 3)]
= (x - 3 (x + 3 - x + 3)
= (x -3)*6
= 6(x - 3)
2)
P(x) = 0 <=> 6(x - 3) = 0
<=> x - 3 = 0
<=> x = 3
S = {3}
