Guide :High School

I know the answer is C. but I need to know how to solve it!

I know the answer is C. but I need to know how to solve it!
Yes you are right it's C)Notice  that f(-2) = (-2)³ +2( - 2)² + 4(-2) + 8 =0Then 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 ...

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