Factoroser. g(x) = 2(2x+3)-(4+2x)-(2x-9)(3-2x)

g(x) = 2(2x+3)-(4+2x)-(2x-9)(3-2x)
g(x) = 4x + 6 - 4 - 2x - (2x - 9) (3 - 2x)
g(x) = 2x + 2 - ( 6x -27 -4x² +18x)
g(x) = 2x + 2 - 6x + 27+ 4x² -18x
g(x) =4x² -22x +29

Le discriminant
Δ = b² - 4ac
Δ = (-22)² − 4×4×29
Δ = 20

√Δ = 2√5

x1 = (-b − √Δ)/2a
x1 = (22 − 2√5) / (8)
x1 = 11/4 − √5 / 4


x2 = (-b + √Δ)/2a
x2 = (22 + 2√5) / (8)
x2 = 11/4 + √5 / 4

Le trinôme admet 4x² − 22x + 29 comme factorisation :

4(x − x1)(x − x2)

Avec :
x1 = 11/4 − √5 / 4

x2 = 11/4 + √5 / 4