Réponse :

développez les expressions suivantes

A = (2 x + 3)(x - 5)

  = 2 x² - 7 x - 15

B = (5 x - 1)(2 x - 3)

   = 10 x² - 17 x + 3

C = 5(2 x + 6) - 3(1 - 5 x)

   = 10 x + 30 - 3 + 15 x

   = 25 x + 27

D = (1 - 4 x)(2 x + 1) - 5(x + 3)

   = 2 x + 1 - 8 x² - 4 x - 5 x - 15

   = - 8 x² - 7 x - 14

E = (2 x - 1)(x + 6) - (1 - x)(x + 6)

  = 2 x² + 11 x - 6 - (x + 6 - x² - 6 x)

  = 2 x² + 11 x - 6 - (- x² - 5 x + 6)

  = 2 x² + 11 x - 6 + x² + 5 x - 6

  = 3 x² + 16 x - 12

F = (x - 1)(2 x + 3)(x + 4)

  = (2 x² + x - 3)(x + 4)

  = 2 x³ + 8 x² + x² + 4 x - 3 x - 12

  = 2 x³ + 9 x² + x - 12

Factorisez

A = 2(2 x + 3) - x(2 x + 3) = (2 x + 3)(2 - x)

B =  5 x² + 3 x = x(5 x + 3)

C = (x+6)(2 x - 1) + 7(2 x - 1) = (2 x - 1)(x + 13)

D = x² + x(x + 1) = x(x + x + 1) = x(2 x + 1)

E = (2 x + 3)(1 - x) - (1 - x)(4 x + 3)

  = (1 - x)(2 x + 3 - 4 x - 3)

  = - 2 x(1 - x)

  = 2 x (x - 1)

F = (2 x - 5)² + 3(2 x - 5)

  = (2 x - 5)(2 x - 5 + 3)

  = (2 x - 5)(2 x - 2)

  = 2(2 x - 5)(x - 1)  

Explications étape par étape