Chapter 8.5, Problem 20PPS

To determine

To factor: The polynomial $5c^{2}v-15c^2{v}^2+5c^2{v}^3$ using the Distributive Property

Answer to Problem 20PPS

  $5c^{2}v\left(1-3v+v^2\right)$

Explanation of Solution

Given:

  $5c^{2}v-15c^2{v}^2+5c^2{v}^3$

Calculation:

The Distributive Property is given by

  $a\left(b+c\right)=ab+ac\text{ and }ab+ac=a\left(b+c\right)$ , where a , b and c are real numbers

Now, in the given polynomial the GCF is $5c^{2}v$

So, factored out the GCF and use the distributive property

  $\begin{array}{l}5c^{2}v-15c^2{v}^2+5c^2{v}^3\\ =5c^{2}v\left(1-3v+v^2\right)\end{array}$

So, the factored form is $5c^{2}v\left(1-3v+v^2\right)$