Chapter 8.5, Problem 38PPS

To determine

To factor: The polynomial $16gh+24g-2h-3$

Answer to Problem 38PPS

  $\left(8g-1\right)\left(2h+3\right)$

Explanation of Solution

Given:

  $16gh+24g-2h-3$

Calculation:

The given polynomial is $16gh+24g-2h-3$

Make groups as shown below

  $\left(16gh-2h\right)+\left(24g-3\right)$

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

  $\begin{array}{l}\left(16gh-2h\right)+\left(24g-3\right)\\ =2h\left(8g-1\right)+3\left(8g-1\right)\\ =\left(8g-1\right)\left(2h+3\right)\end{array}$

So, the factored form is $\left(8g-1\right)\left(2h+3\right)$