Question 232376: Factor completely
x^4 + 2x^3 - 3x -6
Answer by rapaljer(4671)   (Show Source):
You can put this solution on YOUR website! This is a "Factoring by Grouping" problem. Group the first two and the last two terms together. From the first two terms you can take out a common factor of x^3, and from the last two terms you can take out a common factor of -3.
x^4 + 2x^3 -3x -6
x^3(x+2)-3(x+2)
Now notice that you have a COMMON FACTOR of (x+2), so take out the (x+2) factor:
(x+2) (x^3-3)
Since this cannot be factored, this is the FINAL ANSWER!!
For additional help with this VERY important topic of FACTORING, please visit my own website. Do a "Bing" or "Google" search for my last name "Rapalje". Look for "Rapalje Homepage" near the top of the search list. From my Homepage, look for "Basic, Intermediate, and College Algebra: One Step at a Time." Select "Basic Algebra" and look in "Chapter 2" for several topics on Factoring, especially "Factoring the Common Factor" and "Factoring by Grouping." These sections are supported by my "MATH IN LIVING COLOR" pages in which I solved problems IN COLOR!
In addition, I have FREE videos posted of me teaching this topic (a few years ago before I retired!). To see the videos, from my Homepage, look for "Rapalje Videos in Living Color". The videos and the non-traditional explanations are all FREE! I'm not selling anything!!
Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus
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