${x^5 – 4x^3 + x^2 + 3x + 1}$
${x^3 – 3x + 1}$
$x^2$
$-1$
$$
${x^5 -3x^3 +x^2}$
($-$)
($+$) ($-$)
$-x^3 +3x+1$
$-x^3+3x-1$
($+$)
 ($-$) ($+$)  
     ${+2}$
Therefore:${x^5 – 4x^3 + x^2 + 3x + 1 }$ = $(x^3 – 3x + 1)(x^2-1) + 2 $
Since the remainder is not zero, hence first polynomial is a NOT factor of second polynomial.