Chapter 8.5, Problem 12CYU

To determine

To factor: The polynomial $5ab-b-6+30a$

Answer to Problem 12CYU

  $\left(5a-1\right)\left(b+6\right)$

Explanation of Solution

Given:

  $5ab-b-6+30a$

Calculation:

The given polynomial is $5ab-b-6+30a$

Make groups as shown below

  $\left(5ab-b\right)+\left(-6+30a\right)$

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

  $\begin{array}{l}\left(5ab-b\right)+\left(-6+30a\right)\\ =b\left(5a-1\right)+6\left(-1+5a\right)\\ =\left(5a-1\right)\left(b+6\right)\end{array}$

So, the factored form is $\left(5a-1\right)\left(b+6\right)$