Bonjour

Factoriser :

2x^2 + 3x

= 2x * x + 3 * x

= x(2x + 3)

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

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

= (x - 1)(x + 5)

Résolution de chaque inéquation :

2x^2 + 3x < 0

x(2x + 3) < 0

x = 0 ou 2x + 3 = 0

x = 0 ou 2x = -3

x = 0 ou x = -3/2

x.............|-inf........-3/2.......0........+inf

x.............|.......(-)...........(-)...o...(+)........

2x + 3....|.......(-)....o.....(+)......(+)........

Ineq......|........(+)....o.....(-)...o....(+)......

3(x - 1) + (x - 1)(x + 2) > 0

(x + 1)(x + 5) > 0

x + 1 = 0 ou x + 5 = 0

x = -1 ou x = -5

x............|-inf.......-5......-1........+inf

x + 1......|.......(-)........(-)..o...(+)......

x + 5.....|.......(-)...o...(+).......(+)......

Ineq......|.......(+)..o...(-).o.....(+).....