Ira S. answered • 03/26/17

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First off, if x=-8 is a root, then it came from x+8 = 0 which makes (x+8) a factor of your polynomial.

Secondly, complex roots always come in conjugate pairs, so if -i is a root, then so is i and likewise if -5+i is a root then

-5-i is also a root.

So if x=-i is an answer, then x+i = 0 and (x+i) is a factor.

if x=i is an answer, then x-i=0 and (x-i) is a factor.

if x=-5+i is a root, then x+5-i =0 and (x+5-i) is a factor, and

if x=-5-i is a root, then x+5+i =0 and (x+5+i) is a factor.

So just multiply these all out.

(x+8)(x-i)(x+i)(x+5+i)(x+5-i) = 0

multiplying the conjugates makes life a little easier rather than multiplying in order. So,

(x+8)( x

^{2}+1)(x^{2}+10x+26) =0(x+8)(x

^{4}+10x^{3}+27x^{2}+10x+26)=0 and lastly,x

^{5}+ 18x^{4}+107x^{3}+226x^{2}+106x+208=0Hope this helped.