Chapter 8.8, Problem 1P

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

$1.12x^3+3x^2+20x+5$

To determine

To find the GCF of the given polynomial $12x^3+3x^2+20x+5$

Answer to Problem 1P

The GCF of the given polynomial is $\left(4x+1\right)\left(3x^2+5x\right)$ .

Explanation of Solution

Given information:

Given polynomial $12x^3+3x^2+20x+5$

  $\begin{array}{l}\text{Given}12x^3+3x^2+20x+5=3x^2\left(4x+1\right)+5x\left(4x+1\right)\\ =\left(4x+1\right)\left(3x^2+5x\right)\end{array}$

Hence, the GCF of the given polynomial is $\left(4x+1\right)\left(3x^2+5x\right)$ .