Question 695353
{{{f(x)=x^4+2x^3-7x^2+2x-8}}}....factor it

set {{{f(x)=0}}}
replace {{{2x^3}}} with {{{4x^3-2x^3}}} and  {{{-7x^2}}} with {{{x^2-8x^2}}}


{{{x^4+4x^3-2x^3+x^2-8x^2+4x-2x-8}}}..group

{{{(x^4+4x^3)-(2x^3+8x^2)-(x^2+4x)-(2x+8)=0}}}

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

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

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

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

{{{(x^2+1)(x-2)(x+4)=0}}}


solutions:

if {{{x^2+1=0}}}...=>...{{{x^2=-1}}}.=>...{{{x=sqrt(-1)}}}....two complex solutions: {{{i}}} and {{{-i}}}

if {{{x-2=0}}} ...=>...{{{x=2}}}....real solution

if {{{x+4=0}}} ...=>...{{{x=-4}}}...real solution


{{{ graph( 600, 600, -10,10, -50, 10,x^4+2x^3-7x^2+2x-8) }}}