Chapter 8.8, Problem 2P

Find the GCF of the first two terms and the GCF of the last two terms for each polynomial.

$2.6v^3+42v^2+5v+35$

To determine

To find the GCF of the given polynomial $6v^3+42v^2+5v+35$

Answer to Problem 2P

The GCF of the given polynomial is $\left(v+7\right)\left(6v^2+5\right)$ .

Explanation of Solution

Given information:

Given polynomial $6v^3+42v^2+5v+35$

  $\begin{array}{l}\text{Given}6v^3+42v^2+5v+35=6v^2\left(v+7\right)+5\left(v+7\right)\\ =\left(v+7\right)\left(6v^2+5\right)\end{array}$

Hence, the GCF of the given polynomial is $\left(v+7\right)\left(6v^2+5\right)$ .