SOLUTION: Solve the equation {{{x^3+2x^2+x+2=0}}}, if -2 is a root.

Question 175796This question is from textbook
: Solve the equation , if -2 is a root. This question is from textbook

Answer by EMStelley(208) (Show Source): You can put this solution on YOUR website!
If you know that -2 is a root, that means that is a factor of the polynomial. In other words, when you divide by , the remainder will by 0. The easiest way to do this is with synthetic division. Or you could try factoring. I'm not sure of the best way to type synthetic division in here, so I will leave that up to you. Once you complete the division, you get that

So to solve, we get that
and
The first results in x=-2 which we already knew about. So we need to solve the second. All that needs to be done is to subtract the 1 from both side and take the square root.
and
Since the square root of -1 is i, we have that and
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