Exercice d’entraînement – Méthode de factorisation

18x + 24

= 6*3x + 6*4

= 6(3x  + 4)

x³ – 7x

= x ( x² -7)

(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

= (x + 1)(3(2x + 1) -x – 1)

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

(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)

=  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

=x (x² – 1)

=x(x + 1)(x – 1)

(2x + 5)² – (8-x)²

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

=  (3x – 3)  (x + 13 )

= 3 (x – 1)  (x + 13 )