Chapter SH, Problem 14.6.7EP

To determine

To divide: the given expression

Answer to Problem 14.6.7EP

The required result is $6w^2-4w+1$

Explanation of Solution

Given: $\left(24w^3-16w^2+4w\right)÷\left(4w\right)$

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,

  $\left(24w^3-16w^2+4w\right)÷4w=\frac{24w^3-16w^2+4w}{4w}$ .

Divide each term by 4w .

  $\begin{array}{l}\frac{24w^3-16w^2+4w}{4w}=\frac{24w^3}{4w}+\frac{16w^2}{4w}+\frac{4m}{4w}\\ =\frac{24}{4}\cdot \frac{w^3}{w}-\frac{16}{4}\cdot \frac{w^3}{w}\text{+}\frac{4}{4}\cdot \frac{w}{w}\text{ (associative property)}\\ \text{ =6}\cdot w^3-4\cdot w+1\cdot 1\text{ (quotient of powers)}\\ =6w^2-4w+1\text{ (identity)}\end{array}$

Conclusion:Hence, the result is $6w^2-4w+1$ .