Chapter 8.2, Problem 4CYU

To determine

The use of Distributive Property to factor the given polynomial.

Answer to Problem 4CYU

  $2jk\left(6k+3j+jk\right)$

Explanation of Solution

Given:

The given polynomial is:

  $12j{k}^2+6j^{2}k+2j^2{k}^2$

Calculation:

The given polynomial can be factorized using Distributive Property as:

Write the factors of each term:

  $\begin{array}{l}12j{k}^2\\ =2\times 2\times 3\times j\times k\times k\\ 6j^{2}k\\ =2\times 3\times j\times j\times k\\ 2j^2{k}^2\\ =2\times j\times j\times k\times k\end{array}$

Now, take out the common factors from the factors of each term of the polynomial to find the GCF:

  $GCF=2jk$

Write each term as the product of GCF and the remaining factors. Finally use the Distributive Property to factor out the GCF.

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