Chapter 8.5, Problem 4CYU

To determine

To factor: The polynomial $12j{k}^2+6j^{2}k+2j^2{k}^2$ using the distributive property

Answer to Problem 4CYU

  $2jk\left(6k+3j+jk\right)$

Explanation of Solution

Given:

  $12j{k}^2+6j^{2}k+2j^2{k}^2$

Calculation:

The given polynomial is $12j{k}^2+6j^{2}k+2j^2{k}^2$

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 $2jk$

So, factored out the GCF and use the distributive property

  $\begin{array}{l}12j{k}^2+6j^{2}k+2j^2{k}^2\\ =2jk\left(6k+3j+jk\right)\end{array}$

So, the factored form is $2jk\left(6k+3j+jk\right)$