bonsoir
• x^3 + x^2 - 2x - 2 = (x + 1)(ax^2 + bx + c)
x^3 + x^2 - 2x - 2 = ax^3 + bx^2 + cx + ax^2 + bx + c
x^3 + x^2 - 2x - 2 = ax^3 + (a + b)x^2 + (b + c)x + c
a = 1
a + b = 1 => b = 1 - 1 = 0
b + c = -2 => c = -2
x^3 + x^2 - 2x - 2 = (x + 1)(x^2 - 2)
• x^3 + 2x^2 + 4x + 3 = (x + 1)(ax^2 + bx + c)
x^3 + 2x^2 + 4x + 3 = ax^3 + bx^2 + cx + ax^2 + bx + c
x^3 + 2x^2 + 4x + 3 = ax^3 + (a + b)x^2 + (b + c)x + c
a = 1
a + b = 2 => b = 2 - 1 = 1
b + c = 4 => c = 4 - 1 = 3
x^3 + 2x^2 + 4x + 3 = (x - 1)(x^2 + x + 3)
• x^3 + 3x^2 + 2x + 2 = (x + 2)(...)
(-2)^3 + 3 * (-2)^2 + 2 * (-2) + 2
-8 + 3 * 4 - 4 + 2 = 2 et non 0 donc (-2) n’est pas solution
• x^3 + 2x^2 - 3 = (x - 1)(ax^2 + bx + c)
x^3 + 2x^2 - 3 = ax^3 + bx^2 + cx - ax^2 - bx - c
x^3 + 2x^2 - 3 = ax^3 + (b - a)x^2 + (c - b)x - c
a = 1
b - a = 2 => b = 2 + 1 = 3
c - b = 0 => c = 3
x^3 + 2x^2 - 3 = (x - 1)(x^2 + 3x + 3)
• x^3 + 2x^2 - 4x - 8 = (x - 2)(ax^2 + bx + c)
x^3 + 2x^2 - 4x - 8 = ax^3 + bx^2 + cx - 2ax^2 - 2bx - 2c
x^3 + 2x^2 - 4x - 8 = ax^3 + (b - 2a)x^2 + (c - 2b)x - 2c
a = 1
b - 2a = 2 => b = 2 + 2 = 4
c - 2b = -4 => c = -4 + 2 * 4 = -4 + 8 = 4
x^3 + 2x^2 - 4x - 8 = (x - 2)(x^2 + 4x + 4)
• x^3 + 2x^2 - 3x = (x - 1)(ax^2 + bx + c)
x^3 + 2x^2 - 3x = ax^3 + bx^2 + cx - ax^2 - bx - c
x^3 + 2x^2 - 3x = ax^3 + (b - a)x^2 + (c - b)x - c
a = 1
b - a = 2 => b = 2 + 1 = 3
c - b = -3 => c = -3 + 3 = 0
x^3 + 2x^2 - 3x = (x - 1)(x^2 + 3x)
• 2x^3 + 4x^2 + 3x + 1 = (x + 1)(ax^2 + bx + c)
2x^3 + 4x^2 + 3x + 1 = ax^3 + bx^2 + cx + ax^2 + bx + c
2x^3 + 4x^2 + 3x + 1 = ax^3 + (a + b)x^2 + (b + c)x + c
a = 2
a + b = 4 => b = 4 - 2 = 2
b + c = 3 => c = 3 - 2 = 1
2x^3 + 4x^2 + 3x + 1 = (x + 1)(2x^2 + 2x + 1)
• 2x^4 + 4x^3 + 3x^2 + x = (x^2 + x)(ax^2 + bx + c)
2x^4 + 4x^3 + 3x^2 + x = ax^4 + bx^3 + cx^2 + ax^3 + bx^2 + cx
2x^4 + 4x^3 + 3x^2 + x = ax^4 + (a + b)x^3 + (b + c)x^2 + cx
a = 2
a + b = 4 => b = 4 - 2 = 2
b + c = 3 => c = 3 - 2 = 1
2x^4 + 4x^3 + 3x^2 + x = (x^2 + x)(2x^2 + 2x + 1)
