Giải thích các bước giải:
$a, P(x)=2x(x²-1)+x(x+1)+2(x+1)$
$=2x(x-1)(x+1)+x(x+1)+2(x+1)=(x+1)(2x²-2x+x+2)$
$=(x+1)(2x²-x+2)$
$Q(x)=x³+x²+x+1=(x+1)(x²+1)$
$c, Q(x)+R(x)=P(x)$
$⇔R(x)=(x+1)(2x²-x+2)-(x+1)(x²+1)$
$=(x+1)(2x²-x+2-x²-1)=(x+1)(x²-x+1)=x³+1$