Question 400673
<pre><font face = "batangche" color = "indigo" size = 4><b>
15x<sup>4</sup>-10x<sup>2</sup>-30x

Ask yourself: What is the largest whole number that can be divided evenly
into 15, 10, and 30?

Answer: 5

Is it different from 1?

Answer: yes

Then 5 is the first factor of the GCF.

Ask yourself: Is there a letter which appears in every term? 

Answer: yes, x appears in every term.

Then what is the smallest exponent of x?

Answer: The understood exponent 1 in the term -30x which means 
-30x<sup>1</sup> 

Then the GCF is 5x

Then we write

5x(

Then we divide 15x<sup>4</sup> by 5x and get 3x<sup>3</sup>.
So we write this next and we have this:

5x(3x<sup>3</sup>

Then we divide -10x<sup>2</sup> by 5x and get -2x.
So we write this next and we have this:

5x(3x<sup>3</sup>-2x

Then we divide -30x by 5x and get -6.
So we write this next and we have this:

5x(3x<sup>3</sup>-2x-6

We have now divided all the terms by the 5x and so we
end by putting a right parentheses on the right end.
So the final answer is

5x(3x<sup>3</sup>-2x-6)

Edwin</pre>