Question

Solve x^3 + 2x^2 – 4x – 8 = 0.

x = –2, 2

x = –2

x = 2, 2i, –2i

Answer 1

Factor by grouping:
x^3 + 2x^2 − 4x − 8 = (x^3+2x^2) + (−4x−8)
= x^2(x+2) − 4(x+2)
= (x+2)(x^2 − 4)
= (x+2)(x−2)(x+2)
= (x+2)^2(x−2).

Thus the solutions are x = −2 (double root) and x = 2. Among your choices, "x = −2, 2" is correct (with −2 having multiplicity 2).