Réponse :

1) factoriser  A = (4 x - 3)² + 28 x - 21 = (4 x - 3)² + 7(4 x - 3)

= (4 x - 3)(4 x - 3 + 7) = (4 x - 3)(4 x +4) = 4(4 x - 3)(x + 1)

2) B = 3(x +2) + x²+ 4 x + 4 = 3(x+2) + (x +2)² = (x+2)(3 + x + 2) = (x + 2)(x + 5)

3) C = (2 x + 3)(4 +5 x) + 4 x + 6 = (2 x + 3)(4 +5 x) + 2(2 x + 3)

        = (2 x + 3)(4+5 x + 2) = (2 x + 3)(5 x + 6)

     D = 5 x - 7 + (7 - 5 x)² = - (7 - 5 x) + (7 - 5 x)²

         = (7 - 5 x)(- 1 + 7 - 5 x) = (7 - 5 x)(6 - 5 x)

     E = (5 x+2)(x+1) + x²+2 x + 1 = (5 x+2)(x+1) + (x + 1)²

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

     F = x² + 6 x + 9 - (2 x - 3)(x + 3) = (x+3)² - (2 x - 3)(x+3)

         = (x+3)(x+3 - 2 x + 3) = (x+3)(6 - x)

     G = (3 x + 2)(4 x - 1) + (8 x - 2)(7 x - 8) = (3 x + 2)(4 x - 1) + 2(4 x - 1)(7 x - 8)

         = (4 x - 1)(3 x + 2 + 2(7 x - 8)) = (4 x - 1)(3 x + 2 + 14 x - 16)

         = (4 x - 1)(17 x  - 14)  

Explications étape par étape