N'étant pas très forte en Mathématiques, j'aurais que quelqu'un m'aide pour mon dm, merci d'avance. :) (niveau seconde)

1) développer réduire et ordonner :

f(x) = (x - 2)(2x + 3) - (x - 2)(x + 4)
f(x) = 2x^2 + 3x - 4x - 6 - (x^2 + 4x - 2x - 8)
f(x) = 2x^2 - x - 6 - x^2 - 2x + 8
f(x) = x^2 - 3x + 2

2) factoriser

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

3) f(x) = (x - 3/2)^2 - 1/4
f(x) = (x - 3/2 - 1/2)(x - 3/2 + 1/2)
f(x) = (x - 4/2)(x - 2/2)
f(x) = (x - 2)(x - 1)

4) a) f(0) et f(3/2) :

f(0) = (0 - 2)(0 - 1)
f(0) = (-2) * (-1)
f(0) = 2

f(3/2) = (3/2 - 3/2)^2 - 1/4
f(3/2) = 0 - 1/4
f(3/2) = -1/4

b) résoudre f(x) = 0

(x - 2)(x - 1) = 0
x - 2 = 0
x = 2

x - 1 = 0
x = 1

c) résoudre f(x) = 2
x^2 - 3x + 2 = 2
x^2 - 3x = 2 - 2
x^2 - 3x = 0
x(x - 3) = 0
x = 0
Et
x - 3 = 0
x = 3

d) résoudre f(x) = x - 2

x^2 - 3x + 2 = x - 2
x^2 - 3x - x + 4 = 0
x^2 - 4x + 4 = 0
(x)^2 - 2 * 2 * x + (2)^2 = 0
(x - 2)^2 = 0

x - 2 = 0
x = 2

e) résoudre f(x) = 6 :

(x - 3/2)^2 - 1/4 = 24/4
(x - 3/2)^2 - 1/4 - 24/4 = 0
(x - 3/2)^2 - 25/4 = 0
(x - 3/2)^2 - (5/2)^2 = 0
(x - 3/2 - 5/2)(x - 3/2 + 5/2) = 0
(x - 8/2)(x + 2/2) = 0
(x - 4)(x + 1) = 0

x - 4 = 0
x = 4

x + 1 = 0
x = -1