Chapter SH, Problem 14.6.8EP

To determine

To divide: the given expression

Answer to Problem 14.6.8EP

The required result is $16n^2+8n-3$

Explanation of Solution

Given: $\left(16n^3+8n^2-3n\right)÷n$

Calculation:

Essential understanding:

To divide a polynomial by a monomial, divide each term of the polynomial by the monomial.

  $\frac{a+b}{c}=\frac{a}{c}+\frac{b}{c}$ .

Write the rational expression,

  $\left(16n^3+8n^2-3n\right)÷n=\frac{16n^3+8n^2-3n}{n}$

Divide each term by n .

  $\begin{array}{l}\frac{16n^3+8n^2-3n}{n}=\frac{16n^3}{n}+\frac{8n^2}{n}+\frac{3n}{n}\\ =\frac{16}{1}\cdot \frac{n^3}{n}+\frac{8}{1}\cdot \frac{n^2}{n}-\frac{3}{1}\cdot \frac{n}{n}\text{ (associative property)}\\ \text{ =16}\cdot n^2+8\cdot n-3\cdot 1\text{ (quotient of powers)}\\ =16n^2+8n-3\text{ (identity)}\end{array}$

Conclusion:Hence, the result is $16n^2+8n-3$ .