Question 910555
first find roots:

{{{x^3-4x^2+3x+2=0}}} write {{{-4x^2}}} as {{{-2x^2-2x^2}}} and {{{3x}}} as {{{4x-x}}}

{{{x^3-2x^2-2x^2+4x-x+2=0}}} group

{{{(x^3-2x^2)-(2x^2-4x)-(x-2)=0}}}

{{{x^2(x-2)-2x(x-2)-(x-2)=0}}}

{{{(x-2)(x^2-2x-1)=0}}}

if {{{x-2=0}}} => {{{x=2}}} first root

to find other two zeros solve {{{x^2-2x-1=0}}} using quadr. formula


{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 


{{{x = (-(-2) +- sqrt((-2)^2-4*1*(-1) ))/(2*1) }}} 


{{{x = (2 +- sqrt(4+4 ))/2 }}} 

{{{x = (2 +- sqrt(2*4 ))/2 }}} 

{{{x = (2 +- 2sqrt(2 ))/2 }}} 

{{{x = (cross(2) +- cross(2)sqrt(2 ))/cross(2) }}} 

{{{x = (1 +- sqrt(2 )) }}}

{{{x = (1 +- 1.41) }}}


second root: {{{x = 1 + 1.41=2.41 }}}

third root: {{{x = 1 - 1.41=-0.41 }}}


now make all two more:

first root {{{x=2}}} => two more will be {{{x[1]=4}}}

second root: {{{x =2.41 }}} => two more will be {{{x[2] =4.41 }}} 

third root: {{{x =-0.41 }}} => two more will be {{{x[3] =1.59 }}}

Find the equation using roots:

{{{ (x-x[1])(x-x[2])(x-x[3]) }}}

{{{ (x-4)(x-4.41)(x-1.59) }}} multiply all

{{{ (x^2-8.41x+17.64)(x-1.59) }}}

{{{x^3-10x^2+31.0119x-28.0476}}}