Bonjour
P1(1) = 2 * 1^3 - 7 * 1^2 + 2 * 1 + 3
P1(1) = 2 - 7 + 2 + 3
P1(1) = 7 - 7
P1(1) = 0
1 est racine
P1(x) = 2x^3 - 7x^2 + 2x + 3 = (x - 1)(ax^2 + bx + c)
P1(x) = ax^3 + bx^2 + cx - ax^2 - bx - c
P1(x) = ax^3 + (b - a)x^2 + (c - b)x - c
a = 2
b - a = -7 => b = -7 + a = -7 + 2 = -5
c - b = 2 => c = 2 + b = 2 - 5 = -3
-c = 3 => c = -3
P1(x) = (x - 1)(2x^2 - 5x - 3)
P2(1) = 1^3 - 9 * 1^2 + 24 * 1 - 16
P2(1) = 1 - 9 + 24 - 16
P2(1) = 25 - 25
P2(1) = 0
1 est racine
P2(x) = x^3 - 9x^2 + 24x - 16 = (x - 1)(ax^2 + bx + c)
P2(x) = ax^3 + (b - a)x^2 + (c - b)x - c
a = 1
b - a = -9 => b = -9 + a = -9 + 1 = -8
c - b = 24 => c = 24 + b = 24 - 8 = 16
-c = -16 => c = 16
P2(x) = (x - 1)(x^2 - 8x + 16)
P3(1) = 4 * 1^3 + 8 * 1^2 - 2 * 1 - 10
P3(1) = 4 + 8 - 2 - 10
P3(1) = 12 - 12
P3(1) = 0
1 est racine
P3(x) = 4x^3 + 8x^2 - 2x - 10 = (x - 1)(ax^2 + bx + c)
P3(x) = ax^3 + (b - a)x^2 + (c - b)x - c
a = 4
b - a = 8 => b = 8 + a = 8 + 4 = 12
c - b = -2 => c = -2 + b = -2 + 12 = 10
-c = -10 => c = 10
P3(x) = (x - 1)(4x^2 + 12x + 10)
