Let [tex]$a(x)=5x^2-6x+10x-2$[/tex], and [tex]$b(x)=15x^3+2x$[/tex].
When dividing [tex][tex]$a$[/tex][/tex] by [tex]$b$[/tex], we can find the unique quotient polynomial [tex]$q$[/tex] and remainder polynomial [tex][tex]$r$[/tex][/tex] that satisfy the following equation:
[tex]\frac{a(x)}{b(x)}=q(x)+\frac{r(x)}{b(x)},[/tex]
where the degree of [tex]$r(x)$[/tex] is less than the degree of [tex]$b(x)$[/tex].
What is the quotient, [tex][tex]$q(x)$[/tex][/tex]?
[tex]q(x)=[/tex] [tex]$\square$[/tex]
What is the remainder, [tex]$r(x)$[/tex]?
[tex]r(x)=[/tex] [tex]$\square$[/tex]