Chapter 8.5, Problem 18PPS

To determine

To factor: The polynomial $5z^2+10z$ using the Distributive Property

Answer to Problem 18PPS

  $5z\left(z+2\right)$

Explanation of Solution

Given:

  $5z^2+10z$

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 $5z$

So, factored out the GCF and use the distributive property

  $\begin{array}{l}5z^2+10z\\ =5z\left(z+2\right)\end{array}$

So, the factored form is $5z\left(z+2\right)$