FICHE METHODE : Comment factoriser une expression

Corrigé de la fiche bilan du chapitre 7 : factorisations |Exercice 1 : |B = 25x + 15 |C =6x - 2 |
|A = x² - 3x |B = 5×5x + 5×3 |C = 2×3x - 2×1 |
|A = x×x - 3x |B = 5( 5x + 3) |C = 2(3x - 1) |
|A = x( x - 3) | | |
|D = ( 5 x - 1 )( x + 7 ) - (|E = ( x + 1 )( 2 x - 3 ) - ( |
|5 x - 1 )× 1 |x + 1 )2 |
|D = ( 5x - 1) [ ( x + 7) - |E = (x + 1)(2x - 3) - (x + |
|1] |1)(x + 1) |
|D = ( 5x - 1)( x + 7 - 1) |E = (x + 1)[(2x - 3) - (x + |
|D = 5x - 1)(x + 6) |1)] |
| |E = (x + 1)[ 2x - 3 - x - 1] |
| |E = (x + 1)(x - 4) |
F = 3(2x - 5)² + (2x - 5)× 7 F = 3(2x - 5)(2x - 5) + (2x - 5)×7 F = (2x - 5) [ 3(2x - 5) + 7] F = (2x - 5) [ 6x - 15 + 7] F = (2x - 5)(6x - 8) |Exercice 2 : |H = 81x² + 16 - |I = 64 - x² |
|G = 4 x2 + 12 x + 9|72x |I = (8 - x)(8 + x) |
| |H = 81x² - 72x + 16| |
|G = (2x + 3)² | | |
| |H = (9x - 4)² | |
|J = (3x + 4)² - 100 |K = 25 - ( 2x - 1)² |
|J = (3x + 4)² - 10² |K = 5² - (2x - 1)² |
|J = [(3x + 4) - 10][(3x + 4)|K = [ 5 - (2x - 1)][5 + (2x |
|+ 10] |- 1)] |
|J = [3x + 4 - 10][3x + 4 + |K = [ 5 - 2x + 1][5 + 2x - |
|10] |1] |
|J = (3x - 6)(3x + 14) |K = (- 2x + 6)(2x + 4) |
|L = ( x + 1 )2 - ( 2 x + 6 )2 |M = x² - 9( 5x - 7)² |
|L = [(x + 1) - (2x + 6)] [ (x + 1)|M = x² - 3²(5x - 7)² |
|+ (2x + 6)] |M = x² - [3(5x - 7)]² |
|L = [x + 1 - 2x - 6][x + 1 + 2x + |M = x² - (15x - 21)² |
|6) | |
|L = (- x - 5)(3x + 7) | |
M = [ x - (15x - 21)][x + (15x - 21)] M = [ x - 15x + 21][x + 15x - 21] M = (- 14x + 21)(16x - 21) |Exercice 3 : |O = x² + 2x + 1 - 3(x + 1) |
|N = x2 - 4 + ( x + 2 )( 4 - |O = (x + 1)² - 3(x + 1) |
|3 x ) |O = (x + 1)(x + 1) - 3(x + |
|N = (x - 2)(x + 2) + (x + |1) |
|2)(4 - 3x) |O = (x + 1)[ (x + 1) - 3] |
|N = (x + 2)[(x - 2) + (4 - |O = (x + 1)(x + 1 - 3) |
|3x)] |O = (x + 1)(x - 2) |
|N = (x + 2)[x - 2 + 4 - 3x) | |
|N = (x + 2)(- 2x + 2) | |
P = 9x² - 6x + 1 - ( x² + 8x + 16) P = (3x - 1)² - (x + 4)² P = [ (3x - 1) - (x + 4)][(3x - 1) + (x + 4)] P = [ 3x - 1 - x - 4][3x - 1 + x + 4] P = (2x - 5)(4x + 3) |Exercice 4 : |R = (5x - 8)² - ( 10x - 16|
|Q = ( 2 x + 1 )( 1 - x ) + ( 2 |) |
|- 2 x )( x + 3 ) |R = (5x - 8)(5x - 8) - |
|Q = (2x + 1)(1 - x) + 2(1 - |2(5x - 8) |
|x)(x + 3) |R = (5x - 8)[(5x - 8) - 2]|
|Q = (1 - x)[(2x + 1)+ 2(x + 3)]| |
| |R = (5x - 8)[5x - 8 - 2] |
|Q = (1 - x)[ 2x + 1 + 2x + 6] |R = (5x - 8)(5x - 10) |
|Q = (1 - x)(4x + 7) | |
|S = x3 - 6 x2 + 9 x |T = 2x² - x - (2x - 1)(7 - |
|S = x×x² - x × 6x + 9x |3x) |
|S = x(x² - 6x + 9) |T = x(2x - 1) - (2x - 1)(7 -|
|S = x(x - 3)² |3x) |
| |T = (2x - 1)[ x - (7 - 3x)] |
| |T = (2x - 1)[x - 7 + 3x] |
| |T = (2x - 1)(4x - 7) |