Question 677975
I think you may have meant one of two things. Either the degree is supposed to be 4, or -1 was supposed to be -i.  As you may know, imaginary roots come in conjugate pairs, so with i, we are guaranteed -i to be a root as well. So if -4,-1,i are roots then -i is a root as well, which gives us degree 4.

So I'll solve it both ways.

If you meant -4,-1,i  with degree 4, that's

(x+4)(x+1)(x-i)(x+i)

[x^2+5x+4][x^2+1] = x^4 + 5x^3 + 5x^2 + 5x + 4


If you meant -4,-i,i then that's

(x+4)(x-i)(x+i)

(x+4)(x^2+1) = x^3 + 4x^2+ x + 4