Factoriser les expressions suivantes
A(x) = 9 x² - (x - 1)² ⇔ A = (3 x)² - (x - 1)² c'est une identité remarquable de la forme a² - b² = (a + b)(a - b)
a² = (3 x)² ⇒ a = 3 x
b² = (x - 1)² ⇒ b = (x - 1)
A(x) = (3 x)² - (x - 1)² = (3 x + x - 1)(3 x - x + 1)
= (4 x - 1)(2 x + 1)
B(x) = (3 x - 2)² - 4(x - 1)² ⇔ B(x) = (3 x - 2)² - (2(x - 1))² identité remarquable identique que ci-dessus
B(x) = (3 x - 2)² - (2(x - 1))² = (3 x - 2 + 2(x - 1))(3 x - 2 - 2(x - 1))
B(x) = (3 x - 2 + 2x - 2))(3 x - 2 - 2x + 2))
B(x) = x(5 x - 4)
C(x) = (2 x - 5)(4 x + 3) - (5 x - 3)(2 x - 5)
= (2 x - 5)(4 x + 3 - 5 x + 3)
= (2 x - 5)(6 - x)
D(x) = (5 x - 4)(1 - 2 x) - (1 - 2 x)
= (1 - 2 x)(5 x - 4 - 1)
= (1 - 2 x)(5 x - 5)
= 5(1 - 2 x)(x - 1)
E (x) = (6 x - 1)² - (6 x - 1)
= (6 x - 1)(6 x - 1 - 1)
= (6 x - 1)(6 x - 2)
= 2(6 x - 1)(3 x - 1)
F (x) = (3 - 5 x)² + x(3 - 5 x) - 2(5 x - 3)
⇔F (x) = (3 - 5 x)² + x(3 - 5 x) - 2(- (3 - 5 x))
⇔F (x) = (3 - 5 x)² + x(3 - 5 x) + 2(3 - 5 x)
= (3 - 5 x)(3 - 5 x + x + 2)
= (3 - 5 x)(5 - 4 x)
