Basic Technical Mathematics, 11th Edition

1.9 Division of Algebraic Expressions

• Dividing Monomials • Dividing by a Monomial • Dividing One Polynomial by Another

To find the quotient of one monomial divided by another, we use the laws of exponents and the laws for dividing signed numbers. Again, the exponents may be combined only if the base is the same.

EXAMPLE 1 Dividing monomials

1. $\frac{{\displaystyle 3c^7}}{{\displaystyle c^2}}\hspace{0.17em}=\hspace{0.17em}3c^{7\hspace{0.17em}-\hspace{0.17em}2}\hspace{0.17em}=\hspace{0.17em}3c^5$

2. 

   .9-6 Full Alternative Text

3. $\frac{{\displaystyle \hspace{0.17em}-\hspace{0.17em}6a^{2}x{y}^2}}{{\displaystyle 2ax{y}^4}}\hspace{0.17em}=\hspace{0.17em}\hspace{0.17em}-\hspace{0.17em}\left(\frac{6}{2}\right)\frac{{\displaystyle a^{2\hspace{0.17em}-\hspace{0.17em}1}{x}^{1\hspace{0.17em}-\hspace{0.17em}1}}}{{\displaystyle y^{4\hspace{0.17em}-\hspace{0.17em}2}}}\hspace{0.17em}=\hspace{0.17em}\frac{{\displaystyle \hspace{0.17em}-\hspace{0.17em}3a}}{{\displaystyle y^2}}$

As shown in illustration (c), we use only positive exponents in the final result unless there are specific instructions otherwise.

From arithmetic, we may show how a multinomial is to be divided by ...