Question 200875
<pre>
Hello, I need some help with factoring. I have a couple of problems that are giving me a hard time.

1. Factor completely: x^5y^3 - 3x^4y^2 - 28x^3y  unless I am missing something, I am not finding a GCF for this problem.

2. Factor completely: x^3 - 2x^2 + 6x - 12

Any help will be appreciated.
Thanks in advance.

1. Factor completely: <font color = red><font size = 4><b>x<sup>5</sup>y<sup>3</sup> - 3x<sup>4</sup>y<sup>2</sup> - 28x<sup>3</sup>y

Unfortunately, you were misinformed by the other person who responded. The GCF for the ABOVE is x<sup>3</sup>y, NOT xy</font></font></b>.

We then get: {{{x^5y^3 - 3x^4y^2 - 28x^3y}}} = {{{x^3y(x^2y^2 - 3xy - 28)}}} = {{{x^3y((xy)^2 - 3xy - 28)}}} = {{{highlight_green(x^3y(xy - 7)(xy + 4))}}}

2. Factor completely: <font color = red><font size = 4><b>x<sup>3</sup> - 2x<sup>2</sup> + 6x - 12 </font></font></b>.

We then get: {{{x^3 - 2x^2 + 6x - 12}}} = {{{x^2(x - 2) + 6(x - 2)}}} = {{{highlight_green((x^2 + 6)(x - 2))}}}</pre>