Sagot :
Bonjour ;
Factorisation .
A = 3x + 3 = 3(x + 1) .
B = (x + 1)(x + 5) + 7(x + 1)
= (x + 1)(x + 5 + 7) = (x + 1)(x + 12) .
C = (x + 1)(3x + 4) + (x + 1)(x - 3)
= (x + 1)(3x + 4 + x - 3) = (x + 1)(4x + 1) .
D = (x + 1)(4x + 9) - 5(x + 1)
= (x + 1)(4x + 9 - 5) = (x + 1)(4x + 4)
= 4(x + 1)(x + 1) = 4(x + 1)² .
E = (x + 1)(8x - 3) - (x - 7)(x + 1)
= (x + 1)(8x - 3 - x + 7) = (x + 1)(7x + 4) .
F = (x + 1)(9x - 5)- 7x - 7 = (x + 1)(9x - 5) - 7(x + 1)
= (x + 1)(9x - 5 - 7) = (x + 1)(9x - 12) = 3(x + 1)(3x - 4) .
G = (x + 1)(2x + 4) - (x - 7)(x + 1)
= (x + 1)(2x + 4 - x + 7) = (x + 1)(x + 11) .
H = 2(x + 1)(x - 4) + 3(x + 1)(x + 8)
= (x + 1)(2x - 8) + (x + 1)(3x + 24)
= (x + 1)(2x - 8 + 3x + 24) = (x + 1)(5x + 16) .
I = 7(x + 1)(2x + 1) - 2(x + 1)(3x - 4)
= (x + 1)(14x + 7) - (x + 1)(6x - 8)
= (x + 1)(14x + 7 - 6x + 8) = (x + 1)(8x + 15) .
J = 3(x + 5)(x + 1) + 4x + 4 = (x + 1)(3x + 15) + 4(x + 1)
= (x + 1)(3x + 15 + 4) = (x + 1)(3x + 19) .
K = 2(x + 8)(x + 1) + x + 1 = (2x + 16)(x + 1) + (x + 1)
= (x + 1)(2x + 16 + 1) = (x + 1)(2x + 17) .
L = (x + 1)² + x + 1 = (x + 1)(x + 1) + (x + 1)
= (x + 1)(x + 1 + 1) = (x + 1)(x + 2) .
M = (x + 1)(x - 1) + (2x - 6)(3x + 3) = (x + 1)(x - 1) + 3(x + 1)(2x - 6)
= (x + 1)(x - 1) + (x + 1)(6x - 18) = (x + 1)(x - 1 + 6x - 18)
= (x + 1)(7x - 19) .
N = (x + 1)(5x + 9) + (4x - 7)(- 3x - 3) = (x + 1)(5x + 9) - 3(x + 1)(4x - 7)
= (x + 1)(5x + 9 ) - (x + 1)(12x - 21) = (x + 1)(5x + 9 - 12x + 21)
= (x + 1)(- 7x + 30) .
P = (x + 1)² + x² - 1
= (x + 1)(x + 1) + (x + 1)(x - 1) identité remarquable a² - b² = (a - b)(a + b)
= (x + 1)(x + 1 + x - 1) = 2x(x + 1) .
Q = x² + 2x + 1 + 3(x + 1)
= (x + 1)² + 3(x + 1) identité remarquable a² + 2a + 1 = (a + 1)²
= (x + 1)(x + 1) + 3(x + 1) = (x + 1)(x + 1 + 3) = (x + 1)(x + 4) .
R = (x + 1)(x + 9) - x - 1 = (x + 1)(x + 9) - (x + 1)
= (x + 1)(x + 9 - 1) = (x + 1)(x + 8) .
S = 3x² - 3 + x + 1 = 3(x² - 1) + (x + 1)
= 3(x + 1)(x - 1) + (x + 1) identité remarquable a² - 1 = (a + 1)(a - 1)
= (x + 1)(3x - 3) + (x + 1) = (x + 1)(3x - 3 + 1)
= (x + 1)(3x - 2) .
T = (2x + 2)² + x + 1 = (2(x + 1))² + (x + 1)
= 2²(x + 1)² + (x + 1) = 4(x + 1)(x + 1) + (x + 1)
= (x + 1)(4x + 4) + (x + 1) = (x + 1)(4x + 4 + 1)
= (x + 1)(4x + 5) .
U = [tex]x^4[/tex] - 1 = (x²)² - 1²
= (x² - 1)(x² + 1) identité remarquable a² - b² = (a - b)(a + b)
= (x - 1)(x + 1)(x² + 1) la même identité remarquable .
Développement et réduction .
C = (x + 1)(3x + 4) + (x + 1)(x - 3)
= 3x² + 4x + 3x + 4 + x² - 3x + x - 3
= 4x² + 5x + 1 .
D = (x + 1)(4x + 9) - 5(x + 1)
= 4x² + 9x + 4x + 9 - 5x - 5
= 4x² + 8x + 4 .
G = (x + 1)(2x + 4) - (x - 7)(x + 1)
= 2x² + 4x + 2x + 4 - x² - x + 7x + 7
= x² + 12x + 11 .
H = 2(x + 1)(x - 4) + 3(x + 1)(x + 8)
= 2(x² - 4x + x - 4) + 3(x² + 8x + x + 8)
= 2(x² - 3x - 4) + 3(x² + 9x + 8)
= 2x² - 6x - 8 + 3x² + 27x + 24
= 5x² + 21x + 16 .
J = 3(x + 5)(x + 1) + 4x + 4
= 3(x² + x + 5x + 5) + 4x + 4
= 3(x² + 6x + 5) + 4x + 4
= 3x² + 18x + 15 + 4x + 4
= 3x² + 22x + 19 .
N = (x + 1)(5x + 9) + (4x - 7)(- 3x - 3)
= 5x² + 9x + 5x + 9 - 12x² - 12x + 21x + 21
= - 7x² + 23x + 30 .
P = (x + 1)² + x² - 1
= x² + 2x + 1 + x² - 1 identité remarquable (a + 1)² = a² + 2a + 1
= 2x² + 2x .
T = (2x + 2)² + x + 1
= (2x)² + 2 * 2 * 2x + 2² + x + 1 identité remarquable
= 4x² + 8x + 4 + x + 1
= 4x² + 9x + 5 .
