Question 553747: what is the factor of 8x^2+67x-45? I cannot break it down any further.
Found 2 solutions by stanbon, rapaljer:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! what is the factor of 8x^2+67x-45
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I graphed it and found a Real Number zero at x = 9
The other root is 5/8.
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Factor Form:
(x+9)(8x-5) = 0
x = -9 or x = 5/8
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Cheers,
Stan H.
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Answer by rapaljer(4671)  (Show Source):
You can put this solution on YOUR website! This is what I call "Advanced Trinomial Factoring". I prefer a trial-and-error method, with a couple of shortcuts.
8x^2+67x-45
Notice that the coefficient of the middle term is an odd number. This means that there can be NO EVEN-EVEN combinations of numbers. So the first times first must be 8x*1x, NOT 2x*4x.
(8x____)(x____)
Now, the last times last must be a product of 45 with opposite signs. This could be 1*45, 3*15, 5*9, or reverse the order of the numbers for more combinations. Whatever you use, multiply one of these numbers times 8 and subtract the other number to end up with 67.
It takes some trial and error, but the combination that works is 5*9, as follows:
(8x-5)(x+9)
In this case, the OUTER TIMES OUTER is 72x, while the INNER TIMES INNER is -5x, and the middle term is indeed 67x.
I hope this helps. For a NON-TRADITIONAL explanation of this topic that is probably easier to understand than your own textbook, please see my own website! The easiest way to find it is to use the easy-to-remember and easy-to-spell link www.mathinlivingcolor.com. At the very bottom of this page there is a link that will take you to the Homepage of my website. I have a complete ALGEBRA curriculum there with LOTS of practice tests, and even a few videos. Best of all, it's all FREE!!!
For this particular topic, which I call "Advanced Trinomial Factoring", when you find the Homepage, look for the link "Basic, Intermediate, and College Algebra: One Step at a Time", choose "Basic Algebra" and look in "Chapter 2" for "Section 2.06 Advanced Trinomial Factoring." Of course, make sure that you understand REGULAR Trinomial Factoring before you do this section. There is a complete explanation, together with lots of examples and exercises with ALL the answers given. You will especially like the "Math in Living Color" pages that go with this, where lots of the hardest exercises are solved for you IN COLOR! I even did a video on this topic before I retired. To see the video, look for "Rapalje Videos in Living Color" on my Homepage, and click on Basic Algebra," and look for the video on "Factoring." As I said, everything on this website is FREE! No pop-ups or advertising!!
If you or anyone needs to contact me, my Email address is rapaljer@seminolestate.edu.
Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus
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