Exercices de factorisation

Factoriser les expressions suivantes :

18x + 24

Corrigé

18x + 24

= 6*3x + 6*4

= 6(3x  + 4)

x3 – 7x

Corrigé

x3 – 7x

= x ( x2 -7)

(x+1)(x-4) – 7(x+1)

Corrigé

(x+1)(x-4) – 7(x+1)

= (x + 1)(x – 4 +(-7))

= (x + 1)(x – 11)

3(x+1)(2x+1) – x(x+1) – x – 1

Corrigé

3(x+1)(2x+1) – x(x+1) – x – 1

= (x + 1)(3(2x + 1) -x – 1)

= (x + 1)(5x + 2)

(x+1)2 + (x+1)(7-x)+ x2 -1

Corrigé

(x+1)2 + (x+1)(7-x)+ x2 -1

= (x+1)2 + (x+1)(7-x)+ (x -1)(x + 1)

= (x+1)((x + 1) + (7-x)+ (x -1))

= (x+1)(x + 7)

3x2 -3 + (x+1)(2x-4) + (x2+2x+1) 

Corrigé

3x2 -3 + (x+1)(2x-4) + (x2+2x+1)

=  3(x -1)(x + 1) + (x+1)(2x-4) + (x + 1)2

=  (x + 1)(3(x – 1) +(2x-4) + (x + 1))

=  (x + 1)(6x  -6) 

= 6 (x + 1)(x  – 1) 

x3 – x

Corrigé

x3 – x

=x (x2 – 1)

=x(x + 1)(x – 1)

(2x + 5)2 – (8-x)2

Corrigé

(2x + 5)2 – (8-x)2

=( (2x + 5) – (8-x) ) ( (2x + 5) + (8-x) )

=  (3x – 3)  (x + 13 )

= 3 (x – 1)  (x + 13 )

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