Let a(x)=-13x^{9}+6x^5+12xa(x)=−13x 9 +6x 5 +12xa, left parenthesis, x, right parenthesis, equals, minus, 13, x, start superscript, 9, end superscript, plus, 6, x, start superscript, 5, end superscript, plus, 12, x, and b(x)=x^6b(x)=x 6 b, left parenthesis, x, right parenthesis, equals, x, start superscript, 6, end superscript. When dividing aaa by bbb, we can find the unique quotient polynomial qqq and remainder polynomial rrr that satisfy the following equation: \dfrac{a(x)}{b(x)}=q(x) + \dfrac{r(x)}{b(x)} b(x) a(x) =q(x)+ b(x) r(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,