Question 322963

First factor : {{{highlight(6b^2)}}}
{{{6b^2(5b+3)=30b^3+18b^2}}}
Subtract this product from the original polynomial to get the remainder,
{{{(30b^3 + 8b^2 + 39b +30)-(30b^3+18b^2)=-10b^2+39b+30}}}
.
.
.
Next factor : {{{highlight(-2b)}}}
{{{-2b(5b+3)= -10b^2-6b}}}
Subtract this product from the remainder to get the new remainder,
{{{(-10b^2+39b+30)-(10b^2-6b)=45b+30}}}
.
.
.
Next factor : {{{highlight(9)}}}
{{{9(5b+3)=45b+27}}}
Subtract this product from the remainder to get the new remainder,
{{{(45b+30)-(45b+27)=highlight_green(3)}}}
.
.
.
No further division is possible, gather the terms and the final remainder,
{{{(30b^3 + 8b^2 + 39b +30)/(5b + 3)=(6b^2-2b+9)+3/(5b+3)}}}