Chapter 8.5, Problem 29PPS

To determine

To factor: The polynomial $21th-3t-35h+5$

Answer to Problem 29PPS

  $\left(7h-1\right)\left(3t-5\right)$

Explanation of Solution

Given:

  $21th-3t-35h+5$

Calculation:

The given polynomial is $21th-3t-35h+5$

Make groups as shown below

  $\left(21th-3t\right)+\left(-35h+5\right)$

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

  $\begin{array}{l}\left(21th-3t\right)+\left(-35h+5\right)\\ =3t\left(7h-1\right)-5\left(7h-1\right)\\ =\left(7h-1\right)\left(3t-5\right)\end{array}$

So, the factored form is $\left(7h-1\right)\left(3t-5\right)$