Bonjour !
3x² + 6 = 3*x² + 3*2 = 3(x²*2)
16x² – 81 = (4x)² - 9² = (4x-9)(4x+9)
5x – 5 = 5*x-5*1 = 5(x-1)
9x² – 5x = x*9x - x*5 = x(9x - 5)
2x – 8 = 2*x - 2*4 = 2(x-4)
12x² + 16x = 4x*3x + 4x * 4 = 4x(3x+4)
3(x-3)+12 = 3(x-3) + 3*4 = 3(x-3+4) = 3(x+1)
4x² – 1 = (2x)² - 1² = (2x-1)(2x+1)
20x² + x = x*20x + x*1 = x(20x+1)
xy + x(y + 1) = x(y+y+1) = x(2y+1)
64 – 49x² = 8² - (7x)² = (8-7x)(8+7x)
Exercice n°2 :Factoriser les expressions suivantes.
A = (7x – 4)(x + 4) + (7x – 4)(3x – 1) = (7x-4)(x+4 +3x-1) = (7x-4)(4x+3)
B = (2x + 1)² + (3x – 8)(2x + 1) = (2x+1)(2x+1 + 3x-8) = (2x+1)(5x-7)
C = (3x + 8)(x + 4) – (x – 1)(3x + 8) = (3x+8)(x+4 - x +1) = 5(3x+8)
D = (x + 5)(6x + 3) – (x + 5) = (x+5)(6x+3-1) = (x+5)(6x+2)
Exercice n°4 :Résoudre les équations suivantes :
1°) 3x + 2 = 6x – 4
<=> 2+4 = 6x-3x
<=> 3x = 6
<=> x = 6/3 = 2
2°) 2x² + 3x = 0
<=> x(2x+3) = 0
x1 = 0, x2 = (0-3)/2 = -1.5
3°)x² = 25
<=> x = √25
x1 = 5, x2 = -5
4°) 5x² – 10x + 2 = 7x + 2
<=> 5x² - 10x +2 -7x -2 = 0
<=> 5x² -17x = 0
<=> x(5x - 17) = 0
x1 = 0, x2 = (0-17)/5 = -3.4
Voilà, j'espère t'avoir aidé.