SOLUTION: The problem says to find all the solutions of the equation with the given value of x as a solution... I am so lost x^3+3x^2+16x-20=0 x=-2+4i

Question 1004969: The problem says to find all the solutions of the equation with the given value of x as a solution... I am so lost
x^3+3x^2+16x-20=0
x=-2+4i
Found 2 solutions by josgarithmetic, MathLover1:
Answer by josgarithmetic(39616) (Show Source): You can put this solution on YOUR website!
(1) Another solution is .
(2) Form the quadratic factor according to the two complex solutions.
(3) Use polynomial division to find the last solution of the equation, using the quadratic expression as divisor and as the dividend.
Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!

using zero product theorem, we can write the 3rd degree function as

given:
...if you have this root, you have to have too (complex roots always in pairs)
then we have

so,

-----------------(
|()
-------------------........subtract
--------------------...........bring down
-------------------...
-------------------......subtract
-------------------.................reminder
so, third product is =>
and your equation is factored as following:

and, roots are:
,
, and

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