Verified answer

Bonjour,

Explications étape par étape :

1. f(x) = x² - 6x - 7

f(x) = x² + x -7x - 7

f(x) = x(x+1) - 7(x+1)

f(x) = (x+1)(x-7)

2. f(x) = -x² + 2x + 8

f(x) = -x² + 2x + 8

f(x) = -x² -2x + 4x + 8

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

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

3. f(x) = -3x² + 5x + 2

f(x) = -3x² -x + 6x + 2

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

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

4. f(x) = 3x² + x +4

[tex]\Delta = b^2 - 4ac = 1^2 - 4 * 3 * 4 = -47 < 0[/tex]

Ce polynôme est irréductible.

5. f(x) = -4x² + 28x – 49

f(x) = -4x² + 14x + 14x - 49

f(x) = -2x(2x-7) + 7(2x-7)

f(x) = (2x-7)(7-2x)

6. f(x) = x² – x-1 ​

[tex]\Delta = b^2 - 4ac = (-1)^2 - 4 * 1 * (-1) = 1 + 4 = 5 > 0[/tex]

[tex]x_1 = \frac{-b-\sqrt{\Delta}}{2a} = \frac{1 - \sqrt{5}}{2}[/tex]

[tex]x_2 = \frac{-b+\sqrt{\Delta}}{2a} = \frac{1 + \sqrt{5}}{2}[/tex]

Forme factorisée : [tex]f(x) = (x-\frac{1 - \sqrt{5}}{2})(x-\frac{1 + \sqrt{5}}{2})[/tex]