## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$y^4-\dfrac{1}{3}y+4$
Divide each term of the trinomial by the divisor to obtain: $\require{cancel} =\dfrac{3y^5}{3y} - \dfrac{y^2}{3y}+\dfrac{12y}{3y}$ Cancel common factors and divide the variables using the quotient rule for exponents ($\frac{a^m}{a^n}=a^{m-n}$) to obtain: $\require{cancel} \\=\dfrac{\cancel{3}y^5}{\cancel{3}y} - \dfrac{y^2}{3y}+\dfrac{\cancel{12}4\cancel{y}}{\cancel{3}\cancel{y}} \\=\dfrac{y^5}{y}-\dfrac{y^2}{3y}+4 \\=y^{5-1}-\dfrac{1}{3}y^{2-1}+4 \\=y^4-\dfrac{1}{3}y+4$