多项式除以单项式（带有余数）

使$a(x)=6x^9-5x^8-12x^3+60$a, left parenthesis, x, right parenthesis, equals, 6, x, start superscript, 9, end superscript, minus, 5, x, start superscript, 8, end superscript, minus, 12, x, cubed, plus, 60，且$b(x)=x^6$b, left parenthesis, x, right parenthesis, equals, x, start superscript, 6, end superscript。

用$a$a除以$b$b，可得到唯一的商多项式$q$q及余数多项式$r$r，并满足以下公式：

$\dfrac{a(x)}{b(x)}=q(x) + \dfrac{r(x)}{b(x)}$start fraction, a, left parenthesis, x, right parenthesis, divided by, b, left parenthesis, x, right parenthesis, end fraction, equals, q, left parenthesis, x, right parenthesis, plus, start fraction, r, left parenthesis, x, right parenthesis, divided by, b, left parenthesis, x, right parenthesis, end fraction,

且$r(x)$r, left parenthesis, x, right parenthesis的幂数低于$b(x)$b, left parenthesis, x, right parenthesis的幂数。

求商多项式$q(x)$q, left parenthesis, x, right parenthesis

$q(x)=$q, left parenthesis, x, right parenthesis, equals

$r(x)=$r, left parenthesis, x, right parenthesis, equals