If a polynomial has zero a, it can be expressed as (x-a)*(some other polynomial). Also, if a polynomial with real coefficients has a complex (non-real) root z, then the conjugate of z is also its root. Conjugate of 2i is -2i.
So, p(x) = a*(x+1)*(x-2i)*(x+2i) = a*(x+1)*(x^2+4) = a*(x^3+x^2+4x+4). Here a is any real number except 0.
Please ask if something is unclear.
Oct 17th, 2015
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