Question 1130355

{{{p(x) = x^3-x^2-4x-6 }}}..........factor

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

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

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

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

zeros:

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

if {{{0 = (x - 3) }}}=>{{{highlight(x=3)}}}

if {{{0 =  (x^2 + 2x + 2)}}}...use quadratic formula

{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}

{{{x = (-2 +- sqrt( 2^2-4*1*2 ))/(2*1) }}}

{{{x = (-2 +- sqrt( 4-8 ))/2 }}}

{{{x = (-2 +- sqrt( -4 ))/2 }}}

{{{x = (-cross(2)1 +- cross(2)i)/cross(2) }}}

{{{x = (-1 +- i)}}}

=>{{{highlight(x = -1 + i)}}} or {{{highlight(x = -1 - i)}}}