Question 763532
{{{f(x)=x^3-7x+6}}}

{{{0=x^3-7x+6}}}.......add {{{3x^2-3x^2}}} and write {{{-7x}}} as {{{-9x+2x}}}

{{{0=x^3+3x^2-3x^2-9x+2x+6}}}...group

{{{0=(x^3+3x^2)-(3x^2+9x)+(2x+6)}}}

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

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

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

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

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

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

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

so, zeros are:

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

if {{{0=x-1}}} => {{{x=1}}}

if {{{0=x+3}}} => {{{x=-3}}}


{{{ graph( 600, 600, -10, 10, -10, 15,(x-2)(x-1)(x+3)) }}}