Question 1011575
{{{f(x)=2x^3+5x^2-x-6}}}....to factor it, first write {{{5x^2}}} as {{{3x^2+2x^2}}} and {{{-x}}} as {{{-4x+3x}}}

{{{f(x)=2x^3+3x^2+2x^2-4x+3x+6}}} group

{{{f(x)=(2x^3+3x^2)+(2x^2+3x)-(4x+6)}}}

{{{f(x)=x^2(2x+3)+x(2x+3)-2(2x+3)}}}

{{{f(x)= (2x+3)  (x^2+x-2)}}}

{{{f(x)= (2x+3)  (x^2+2x-x-2)}}}

{{{f(x)= (2x+3)  ((x^2+2x)-(x+2))}}}

{{{f(x)= (2x+3)  (x(x+2)-(x+2))}}}

{{{f(x)= (2x+3) (x-1) (x+2)}}}

solutions:{{{0= (2x+3) (x-1) (x+2)}}}

if {{{(2x+3)=0}}}=>{{{2x=-3}}}=>{{{x=-3/2}}}
if {{{(x-1)=0}}}=>{{{x=1}}} 
if {{{(x+2)=0}}}=>{{{x=-2}}}


 {{{drawing( 600,600, -5, 5, -10, 10, 
blue(circle(-3/2,0,.1)),blue(circle(1,0,.1)),blue(circle(-2,0,.1)),
 graph( 600,600, -5, 5, -10, 10, (2x+3) (x-1) (x+2))) }}}