Question 18515
 Factor
 {{{ P(X)=X^4+2X^3+6X^2+8X+8 }}}
     = {{{X^4 + 4X^2+ 2X^3 + 2x^2 + 8x + 8}}}
     = {{{X^2(X^2 + 4) + 2x^2(x+1) + 8(x+1)}}}
     = {{{X^2(X^2 + 4) + 2(x+1) (x^2+4)}}}
     = {{{(X^2 + 4)(X^2 + 2X +2) }}}

 Similarly,
{{{ Q(X)=X^4+2X^3+8X^2+8X+16 }}}
 = {{{X^4 + 4X^2+ 2X^3 + 4x^2 + 8x + 16}}}
 = {{{X^2(X^2 + 4) + 2x^2(x+2) + 8(x+2)}}}
 = {{{X^2(X^2 + 4) + 2(x+2) (x^2+4)}}}
 = {{{(X^2 + 4)(X^2 + 2X + 4) }}}

 so
 THE GREATEST COMMON FACTOR IS  {{{ X^2 + 4}}}


 (P(X))/(Q(X))= (____)/(____) ...for you


 Kenny