Question 106206
<pre><font face = "book antiqua" size = 5 color = "indigo"><b>
How do you factor this completely and does it have a GCF? 

x<sup>10</sup>y<sup>3</sup> - 4x<sup>9</sup>y<sup>2</sup> - 21x<sup>8</sup>y

We can factor out the smallest power of any
letter that appears in all three terms.

x and y both appear in all three terms.

The smallest power of x that appears is x<sup>8</sup>
The smallest power of y that appears is y<sup>1</sup> or just y

So we can factor out x<sup>8</sup>y as the GCF

x<sup>8</sup>y(x<sup>2</sup>y<sup>2</sup> - 4xy - 21)

Now we write this:

x<sup>8</sup>y(xy    )(xy    )

Now we think of two positive integers which
multiply to give -21 and have a sum of -4.

These are -7 and +3

So the completely factored form is:

x<sup>8</sup>y(xy - 7)(xy + 3)

Edwin</pre>