Chapter 8.2, Problem 2P

To determine

To find the GCD of the polynomial $3x^4-9x-12x$ .

Answer to Problem 2P

The GCD of the given polynomial is $3x$ .

Explanation of Solution

Given information:

Given polynomial $3x^4-9x-12x$

GCD is the greatest common factor in all the terms of $3x^4-9x-12x$

  $\begin{array}{l}\text{So},3x^4-9x-12x\text{can}\text{be}\text{written}\text{as}\left(3x\right)x^3-\left(3x\right)\left(3x\right)-\left(3x\right)4\\ i.e3x^4-9x-12x=3x\left(x^3-3x-4\right)\end{array}$

Thus, $3x$ is the greatest common factor in all the terms of $3x^4-9x-12x$

Hence, the GCD of the given polynomial is $3x$ .