Chapter 8.5, Problem 25PPS

To determine

To factor: The polynomial $45pq-27q-50p+30$

Answer to Problem 25PPS

  $\left(5p-3\right)\left(9q-10\right)$

Explanation of Solution

Given:

  $45pq-27q-50p+30$

Calculation:

The given polynomial is $45pq-27q-50p+30$

Make groups as shown below

  $\left(45pq-27q\right)+\left(-50p+30\right)$

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

  $\begin{array}{l}\left(45pq-27q\right)+\left(-50p+30\right)\\ =9q\left(5p-3\right)-10\left(5p-3\right)\\ =\left(5p-3\right)\left(9q-10\right)\end{array}$

So, the factored form is $\left(5p-3\right)\left(9q-10\right)$