Răspuns:
Explicație pas cu pas:
a)
E(x) = x^3 + x^2 - 4x - 4 = x^2*(x + 1) - 4*(x + 1) = (x + 1)(x^2 - 4)
= (x + 1)(x + 2)(x - 2)
F(x) = x^3 + 2x^2 - x - 2 = x^2*(x + 2) - (x + 2) = (x + 2)(x^2 - 1)
= (x + 2)(x - 1)(x + 1)
b)
E(x)/F(x) = (x + 1)(x + 2)(x - 2)/(x + 2)(x - 1)(x + 1) = (x - 2)/(x - 1)
x + 2 ≠ 0 ⇒ x ≠ -2
x - 1 ≠ 0 ⇒ x ≠ 1
x + 1 ≠ 0 ⇒ x ≠ -1
x ∈ R \ {-2, -1, 1}
c)
(x + 1)(x + 2)(x - 2) + (x + 2)(x - 1)(x + 1) = 0
(x + 1)(x + 2)(x - 2 + x - 1) = 0
(x + 1)(x + 2)(2x - 3) = 0
x + 1 = 0 ⇒ x = -1
x + 2 = 0 ⇒ x = -2
2x - 3 = 0 ⇒ x = 3/2
A = {-2, -1, 3/2}
