Exercise
$\frac{4y^3+y+27}{2y+3}$
Step-by-step Solution
1
Divide $4y^3+y+27$ by $2y+3$
$\begin{array}{l}\phantom{\phantom{;}2y\phantom{;}+3;}{\phantom{;}2y^{2}-3y\phantom{;}+5\phantom{;}\phantom{;}}\\\phantom{;}2y\phantom{;}+3\overline{\smash{)}\phantom{;}4y^{3}\phantom{-;x^n}+y\phantom{;}+27\phantom{;}\phantom{;}}\\\phantom{\phantom{;}2y\phantom{;}+3;}\underline{-4y^{3}-6y^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-4y^{3}-6y^{2};}-6y^{2}+y\phantom{;}+27\phantom{;}\phantom{;}\\\phantom{\phantom{;}2y\phantom{;}+3-;x^n;}\underline{\phantom{;}6y^{2}+9y\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}6y^{2}+9y\phantom{;}-;x^n;}\phantom{;}10y\phantom{;}+27\phantom{;}\phantom{;}\\\phantom{\phantom{;}2y\phantom{;}+3-;x^n-;x^n;}\underline{-10y\phantom{;}-15\phantom{;}\phantom{;}}\\\phantom{;;-10y\phantom{;}-15\phantom{;}\phantom{;}-;x^n-;x^n;}\phantom{;}12\phantom{;}\phantom{;}\\\end{array}$
$2y^{2}-3y+5+\frac{12}{2y+3}$
Final answer to the exercise
$2y^{2}-3y+5+\frac{12}{2y+3}$