Question 1045163
Assign variables to coefficients and transcribe literally into equations.  Solve the system.  Do not let the formal description of the numbers put you offcourse.  This is a simple linear system  application in three variables.


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The polynomial, {{{ax^3+bx^2+cx+d}}}


The description of the coefficients, {{{system(b=a-3,c=3b,d=a+2,a+b+c+d=-4)}}}


{{{system(a-b=3,c=3b,d=a+2,a+b+c+d=-4)}}}


substituting for c
{{{system(a-b=3,d=a+2,a+b+3b+d=-4)}}}
-
{{{system(a-b=3,d=a+2,a+4b+d=-4)}}}


Substituting for d
{{{system(a-b=3,a+4b+a+2=-4)}}}

{{{system(a-b=3,2a+4b=-6)}}}

{{{system(a-b=3,a+2b=-3)}}}



Partially ready for Elimination Method...subtract first from second.
{{{2b+b=-3-3}}} which eliminated "a".
{{{3b=-6}}}
{{{highlight(b=-2)}}}



{{{b=a-3}}}
{{{a-3=b}}}
{{{a=b+3}}}
{{{a=-2+3}}}
{{{highlight(a=1)}}}


{{{c=3b}}}
{{{c=3*(-2)}}}
{{{highlight(c=-6)}}}


{{{d=a+2}}}
{{{d=1+2}}}
{{{highlight(d=3)}}}



SUMMARY:  The polynomial is {{{highlight_green(highlight(x^3-2x^2-6x+3))}}}.