Explications étape par étape :
EX 1
Trouver le facteur en commun
A = 5x - xy
⇔ A = x . ( 5 - y )
⇔ A = x . ( -y + 5 )
B = a² + 3ab
⇔ B = a . ( a + 3b )
C = 12a - 12ab
⇔ C = 12a . ( 1 - b )
D = 60x³ - 24x⁵ + 36x²
⇔ D = 12x². ( 5x - 2x³ + 3 ) PGDC entre 60 , 24 et 36 : 12
E = 7x² - 28x⁴ + 70x³
⇔ E = 7x². ( 1 - 4x² + 10x )
⇔ E = 7x² . ( -4x² + 10x + 1 )
F = 3 . ( 2 + x ) + ( 2 + x ) . y ( 2 + x ) facteur commun
⇔ F = ( 2 + x ) ( 3 + y )
⇔ F = ( x + 2 ) ( y + 3 )
G = ( x - 3 ) + 2x. ( x - 3 ) ( x - 3 ) facteur commun
⇔ G = ( x - 3 ) ( 1 + 2x )
⇔ G = ( x - 3 ) ( 2x + 1 )
H = ( 5x + 2y ) ( 5 + x ) + 2 .( 5x + 2y )
⇔ H = ( 5x + 2y ) [ ( 5 + x ) + 2 ]
⇔ H = ( 5x + 2y ) ( x + 7 )
EX 2
B = 78x² + 54x⁷ + 42x⁵ PGDC entre 78 ,54 et 42 : 6
⇔ B = 6x² . ( 13 + 9x⁵ + 7x³ ) x² * x⁵ = x²⁺⁵ = x⁷
⇔ B = 6x² . ( 9x⁵ + 7x³ + 13 )
C = 42x⁵y₃ - 30x²y⁷ - 18x⁴y⁴
⇔ C = 6x²y³ . ( 7x³ - 5y⁴ - 3x²y )
D = 45x⁴y⁷z² - 30x³y⁴z + 15x³y³
⇔ D = 15x³y³ . ( 3xy⁴z² - 2yz + 1 )
E = ( 3 - 2x ) ( 5 - x ) - ( 3 - 2x ) ( 7 - 4x ) ( 3 - 2x ) facteur commun
⇔ E = ( 3 - 2x ) . [ ( 5 - x ) - ( 7 - 4x ) ]
⇔ E = ( 3 - 2x ) . ( 5 - x - 7 + 4x )
⇔ E = ( 3 - 2x ) ( 3x - 2 )
⇔ E = ( -2x + 3 ) ( 3x - 2 )
F = ( 7 - 4x ) ( x + 4 ) - ( x + 4 ) ( 7 + 3x )
⇔ F = ( x + 4 ) . [ ( 7 - 4x ) - ( 7 + 3x ) ]
⇔ F = ( x + 4 ) . ( 7 - 4x - 7 - 3x )
⇔ F = ( x + 4 ) . ( -7x )
G = ( 5 + 2x ) ( 5 - x ) - ( 5 + 2x )
⇔ G = ( 5 + 2x )[ ( 5 - x ) - 1 ]
⇔ G = ( 2x + 5 ) ( -x + 4 )
H = ( 7 - 9x ) ( 1 + x ) - 3 ( 7 - 9x )
⇔ H = ( 7 - 9x ) . [ ( 1 + x) - 3 ] ( 7 - 9x ) facteur commun
⇔ H = ( -9x + 7 ) ( x - 2 )
I = ( 2 + x )² + 3.( 2 + x )
⇔ I = ( 2 + x ) [ ( 2 + x ) + 3 ]
⇔ I = ( x + 2 ) ( x + 5 )
