option A. B and C are not the rite one
Polynomial like: ax² + bx + c, where:
a = 3
b = 12
c = 7
Δ = b² - 4ac (discriminant)
Δ = 12² - 4(3 * 7) = 144 - 84 = 60 = 4 * 15
x1 = (- b - √Δ) / 2a = (- 12 - 2√15) / (2 * 3) = (- 6 - √15)/3
x2 = (- b + √Δ) / 2a = (- 12 + 2√15) / (2 * 3) = (- 6 + √15)/3
The polynomial can be written like: a(x - x1)(x - x2)
3x² + 12x + 7 = 3[x - (- 6 - √15)/3] * [x - (- 6 + √15)/3]
3x² + 12x + 7 = [3x - (- 6 - √15)] * [x - (- 6 + √15)/3]
3x² + 12x + 7 = (3x + 6 + √15)[x - (- 6 + √15)/3]
3x² + 12x + 7 = (3x + 6 + √15)[x + (6 - √15)/3]