Answer
Quotient: $3x+3$
Remainder: $2x^2-3x-3$
Work Step by Step
$\space$$\space$$\space$$\space$$\space$$\space$$\space$$\space$$\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space$ ${3x+3}$
$x^3-x^2+0x+1$$\space)\overline{3x^4+0x^3-\space x^2+0x+0}$
$\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\underline{3x^4-3x^3-0x^2+3x}$
$\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space3x^3-\space x^2-3x+0$
$\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\underline{3x^3-3x^2+0x+3}$
$\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space2x^2-3x-3$
Check answer:
$(x^3-x^2+1)\cdot(3x+3)+x^2-3x-3$
$3x^4+3x^3-3x^3-3x^2+3x+3+2x^2-3x-3$
$3x^4-x^2\checkmark$
