Chapter 8.5, Problem 9CYU

To determine

To factor: The polynomial $3km-21k+2m-14$

Answer to Problem 9CYU

  $\left(m-7\right)\left(3k+2\right)$

Explanation of Solution

Given:

  $3km-21k+2m-14$

Calculation:

The given polynomial is $3km-21k+2m-14$

Make groups as shown below

  $\left(3km-21k\right)+\left(2m-14\right)$

So, factored out the GCF from each of the group and then factored out the common factor

  $\begin{array}{l}\left(3km-21k\right)+\left(2m-14\right)\\ =3k\left(m-7\right)+2\left(m-7\right)\\ =\left(m-7\right)\left(3k+2\right)\end{array}$

So, the factored form is $\left(m-7\right)\left(3k+2\right)$