Question 742446
{{{x^4-2x^3-23x^2-2x-24=0}}} write {{{-2x^3}}} as {{{4x^3-6x^3}}},
{{{-23x^2}}} as {{{+x^2-24x^2}}}

{{{x^4+x^2+4x^3+4x-6x^3-6x-24x^2-24=0}}}.....group

{{{(x^4+x^2)+(4x^3+4x)-(6x^3+6x)-(24x^2+24)=0}}}.factor

{{{x^2(x^2+1)+4x(x^2+1)-6x(6x^2+1)-24(x^2+1)=0}}}

{{{(x^2+4x-6x-24)(x^2+1)=0}}}

{{{(x-6)(x+4)(x^2+1)=0}}}

solutions:

if {{{x-6=0}}} => {{{x=6}}}

if {{{x+4=0}}} => {{{x=-4}}}

if {{{x^2+1=0}}} => {{{x^2=-1}}} => {{{x=sqrt(-1)}}}=> {{{x=i}}} or {{{x=-i}}}


{{{ graph( 600, 600, -10, 10, -300, 50, x^4-2x^3-23x^2-2x-24) }}}