Question 221726: I need to factor this expression completely.
27y^5 - 63y^4 + 30y^3
Answer by rapaljer(4671)   (Show Source):
You can put this solution on YOUR website! The first step is ALWAYS to take out the common factor if there is one. In this case, the common factor to each term is 3 y^3.
27y^5 - 63y^4 + 30y^3
3y^3(9y^2 - 21y + 10)
What is left is what I call "Advanced Trinomial Factoring", where the leading coefficient of the trinomial is other than 1. I use a trial and error method.
It could be one of the following possibilities to give you the 9y^2 in the FIRST times FIRST term:
3y^3(3y_____)(3y______) or 3y^3(9y_____)(y_____)
Next, you need to find two numbers whose product is 10. This is probably 5*2, but it could also be 10*1. Let's try the 5*2 combination first:
3y^3(3y_____)(3y______)
3y^3(3y-5)(3y-2)
This one works, since the LAST times LAST is +10, and the MIDDLE TERM will be -6y -15y, which is -21y. It checks!
For additional explanation on Factoring, especially COMMON FACTOR and ADVANCED TRINOMIAL FACTORING, please see my own website. Do a "Bing" search for my last name "Rapalje". Look for "Rapalje Homepage" near the top of the search list. On my Homepage near the top, look for the link "Basic, Intermediate and College Algebra: One Step at a Time." Choose "Basic Algebra", and look in Chapter 2 for sevearl topics on FACTORING. In these sections, you will find my own non-traditional explanations, that my own students all said were a LOT easier to understand than traditional textbooks. See also the corresponding "MATH IN LIVING COLOR" pages in which problems are solved IN COLOR! I also have FREE videos on the website of me teaching my classes a few years ago. To access the videos, go back to my Homepage, and look for the link "Rapalje Videos in Living Color." Select "Basic Algebra", and select the video on "FACTORING."
R^2
Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus
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