correction - Dimension K

Contrôle : calculs littéraux (correction)
EXERCICE 1 (15pts)
A = 8(3x - 4) 0,5pt B = 13x(2x - 4)
0,5pt
=24x - 32 = 26x²-52x C = (6x - 1)² 1pt D = (5x + 3)²
1pt
=36x² - 12x + 1 = 25x² +30x + 9 E = (5y - 6)(5y + 6 ) 1pt F = ( x² - 7 )²
1.5pt
25y² - 36 x4-14x²+49
G = 5(2x - 3)2 + (5x - 2)(5x + 2) 2pt H = x + ) 2
2pt
=5(4x²-12x+9) + 25x² - 4 =[pic]
=20x²-60x+45 + 25x² - 4 = 45x²-60x +41 I = 8(2x - 1)(2x + 1) - 4(3x - 1)2 2,5pt J = (106+10-
5)² 1pt
=8(4x²-1)-4(9x²-6x+1) = 1012+2×101+10-10
=32x² - 8 - 36x² +24x -4 = -4x²+24x -12 K = (5x -4)(3x-2)(5x + 4) 2pt
= (25x²-16)(3x-2)
=75x3 - 50x² -48x +32 EXERCICE 2 (27pts)
A = 13x - 13y 0,5pt B = 5x + 5
0,5pt
=13(x-y) =5(x+1) C = 12xy - 18yz 1pt D = 4x² + 12x + 9
1,5pt
=2y(6x-9z) =(2x+3)² E = 81x² - 4 1,5pt F = 25x² + 4 - 20x
2 pt
=(9x -2)(9x+2) =(5x-2)²
G = (2x - 7)² - 121 2,5pt H = [pic] 2,5 pt
=[(2x-7)-11][(2x-7)+11] =[pic]
=[2x-18][2x+4] = 4(x-9)(x+2) I = (51z - 1)(3x-5) - (51z - 1)(7x + 3) 2pt J = 9(x - 1)2 -
16(x + 1)2 2,5 pt
=(51z-1)[(3x-5)-(7x+3)] = [3(x - 1)]2 - [4(x +
1)]2
=(51z-1)[3x-5-7x-3] = [(3x-3) - (4x+4)][(3x-
3)+(4x+4)]
=(51z-1)[-4x-8] = -4(51z-1)[x+2] = [-x-7][7x+1] K= 18x² + 60x +50 2,5pt L = (5x - 1) - 2(5x -
1)(x + 3) 2pt
=2(9x²+30x+25) =(5x-1)[1-2(x+3)]
=2(3x+5)² =(5x-1)[1-2x-6] =(5x-1)[-
7-2x] L =[pic] M = (3x - 2) (x + 2) + x ² - 4 3 pt
=[pic] = (3x - 2) (x + 2) + (x - 2) (x + 2)
=[pic] = (x + 2) [(3x - 2) + (x - 2)]
=[pic] = (x + 2) [4x - 4] = 4(x + 2) [x - 1] EXERCICE 3 (4pts)
Soit l'expression O = (2x + 7)(x - 4) + 4x² + 28x + 49.
a) O = 2x²-8x + 7x -28 + 4x² + 28x + 49 = 6x² + 27x + 21
b) 4x² + 28x + 49 = (2x + 7)²
c) O = (2x + 7)(x - 4) + (2x + 7)²
= (2x + 7)[(x - 4) + (2x + 7)]
= (2x + 7)( 3x + 3 )
EXERCICE 4 (7pts)
V =[pic] 3,5 pt W = [pic] 3,5 pt
= [pic] =[pic]
= [pic] =[pic]
EXERCICE 5 (7,5pts)
Simplifiez les fractions suivantes :
X =[pic] 2,5 pt Y = [pic] 2,5 pt Z = [pic] 2,5 pt
=[pic] = [pic] = [pic]
=[pic] = [pic] = [pic]
=[pic] = [pic] = [pic]