Chapter 8.8, Problem 8P

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

$21x^3-28x^2-6x+8$

To determine

To find the GCF of the given polynomial $21x^3-28x^2-6x+8$

Answer to Problem 8P

The GCF of the given polynomial is $\left(3x-4\right)\left(7x^2-2\right)$ .

Explanation of Solution

Given information:

Given polynomial $21x^3-28x^2-6x+8$

  $\begin{array}{l}\text{Given}21x^3-28x^2-6x+8=7x^2\left(3x-4\right)-2\left(3x-4\right)\\ =\left(3x-4\right)\left(7x^2-2\right)\end{array}$

Hence, the GCF of the given polynomial is $\left(3x-4\right)\left(7x^2-2\right)$ .