Yes you are right it's C) Notice that f(-2) = (-2)³ +2( - 2)² + 4(-2) + 8 =0 Then x³+2x²+4x+8 is divisible by (x+2) Perform this division & you will get:
x³+2x²+4x+8 = (x+2)(x²+4) The root of (x+2) is the value that render it nil, that is x=-2 The root of (x²+4) are imaginary (not real) because x²+4 =0 ==> x² = -4 & x=√-4 or x= 2i (nor real). Hope you understood the reasoning
