Bonjour,
1) f(x) = (3x - 5) ( 3x + 5) - (-2x + 3) (3x - 5)
f(x) = 9x² + 15x - 15x - 25 + 6x² - 10x - 9x + 15
f(x) = 15x² - 19x - 10
2) f(x) = (3x - 5) ( 3x + 5) - (-2x + 3) (3x - 5)
f(x) = (3x - 5) ( 3x + 5 + 2x - 3)
f(x) = (3x - 5) ( 5x + 2)
3.a) Expression factorisée
f(x) = 0 ⇔ (3x - 5) ( 5x + 2) = 0
⇔ 3x - 5 = 0 ou 5x + 2 = 0
⇔ x = 5/3 ou x = -2/5
b) expression développée
f(√2) = 15(√2)² - 19√2 - 10 = 30 - 19√2 - 10 = 20 - 19√2
c) expression développée
f(x) = -10 ⇔ 15x² - 19x - 10 = -10
⇔ 15x² - 19x = 0
⇔ x (15x - 19) = 0
⇔ x = 0 ou x = 19/15
