Question 1000536
 

{{{9x^4-18x^3+17x^2-18x+8=0}}}.......factor completely,..first write {{{-18x^3}}} as {{{-6x^3-6x-12x^3}}}, {{{17x^2}}} as {{{9x^2+8x^2}}}, and {{{-18x}}} as {{{-6x-12x}}}

 {{{9x^4-6x^3-6x-12x^3+9x^2+8x^2-6x-12x+8=0}}}......group
 {{{(9x^4+ 9x^2)-(12x^3+12x)-(6x^3+6x)+(8x^2+8)=0}}}
 {{{9x^2(x^2+ 1)-12x(x^2+1)-6x(x^2+1)+8(x^2+1)=0}}}
{{{(9x^2-6x-12x+8)(x^2+1) = 0}}}
{{{((9x^2-6x)-(12x-8))(x^2+1) = 0}}}
{{{(3x(3x-2)-4(3x-2))(x^2+1) = 0}}}
{{{(3x-4) (3x-2) (x^2+1) = 0}}}

solutions:

if {{{(3x-4)  = 0}}}=>{{{3x=4}}}=>{{{highlight(x=4/3)}}}
if {{{(3x-2)  = 0}}}=>{{{3x=2}}}=>{{{highlight(x=2/3)}}}
if{{{ (x^2+1) = 0}}}=>{{{x^2=-1}}}=>{{{x=sqrt(-1)}}}=>{{{highlight(x=i)}}} and {{{highlight(x=-i)}}}