Question 1131619


Which shows one way to determine the factors of {{{x^3 + 11x^2 - 3x -33}}} by grouping?

take a look on coefficients: 

{{{1*x^3 }}}-> prime, divisible by {{{1}}}
{{{11x^2}}}->prime, divisible by {{{1}}} and {{{11}}}
{{{ - 3x }}}->prime, divisible by {{{1}}} and {{{3}}}
{{{-33}}} -> divisible by {{{1}}} ,{{{3}}} and {{{33}}}

so, the best way is to group those with common factors:

 {{{1*x^3 }}} with {{{- 3x}}}
and
{{{  11x^2}}} with {{{-33}}}


{{{(x^3 - 3x) + (11x^2 -33)}}} 

{{{x(x^2 - 3) + 11(x^2 -3)}}} 

{{{(x + 11)(x^2 -3)}}}