Question 1032754
<pre><b>
{{{x^3-x^2}}}{{{""=""}}}{{{18}}}

{{{x^3-x^2-18}}}{{{""=""}}}{{{0}}}

{{{x^3-x^2+0x-18}}}{{{""=""}}}{{{0}}}

Potential rational solutions: ±1,±3,±6,±9,±18

3|1 -1  0 -18
 |<u>   3  6  18</u>
  1  2  6   0

We have factored the polynomial as

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

Use zero-factor property:

{{{x-3}}}{{{""=""}}}{{{0}}}; {{{x^2+2x+6}}}{{{""=""}}}{{{0}}}

{{{x}}}{{{""=""}}}{{{3}}};   {{{x}}}{{{""=""}}}{{{(-b +- sqrt(b^2-4ac ))/(2a) }}}

                  {{{x}}}{{{""=""}}}{{{(-2 +- sqrt(2^2-4(1)(6) ))/(2(1)) }}}
                  {{{x}}}{{{""=""}}}{{{(-2 +- sqrt(4-24))/2 }}}
                  {{{x}}}{{{""=""}}}{{{(-2 +- sqrt(-20))/2 }}}
                  {{{x}}}{{{""=""}}}{{{(-2 +- i*sqrt(20))/2 }}}
                  {{{x}}}{{{""=""}}}{{{(-2 +- i*sqrt(4*5))/2 }}}
                  {{{x}}}{{{""=""}}}{{{(-2 +- 2i*sqrt(5))/2 }}}
                  {{{x}}}{{{""=""}}}{{{-2/2 +- 2i*sqrt(5)/2 }}}
                  {{{x}}}{{{""=""}}}{{{-1 +- i*sqrt(5) }}}

Solution set {{{matrix(1,7,

"{",3,",",-1+i*sqrt(5),",",-1-i*sqrt(5),"}")}}} 

Edwin</pre></b>