In the seven-minute video, he actually explains what lower and upper bounds are. More than I can say for my pre-calc teacher. BTW the examples start at 2:54.
Why did he choose -4 and 5? I thought it was that Therom that states it’s the factors of the leading term and the last term but 5 isn’t a factor of 1 neither 48? So any ideas why?
Divide the last term by the first term of the polynomial. In this case look for all the factors of 48 and divide that by the factors of 1. So, it will be plus and minus 48, plus and minus 24, plus and minus 12.... Etc etc. and divide that by plus and minus 1. That's how he divided by -4 to begin with.
Ikhine Stephen No, the 5 was just a test, he knew it wasn't going to divide into distributively (meaning that there was going to reminder). You noticed that that when he divided by 5 (a nonnegative number), his quotient (answer) and his remainder (last number next to quotient) were nonnegative. This proved the upper bound theorem. In other words, there can be no other nonnegative number larger than 5 that can divide into this polynomial. So if you want to find a real zero for this polynomial, you best believe that it will have to be below the positive number "5".
The possible factors of 48 are -48,-24,-16,-12,-8,-6,-4,-3,-2,-1,1,2,3,4,6,8,12,16,24, and 48. That's 20 possible solutions. So you would want to start with maybe -6, or -4 for a lower bound. He used -4. He should have then tested -3 and it would not work so he would know -4 was the greatest lower bound. He should have then started with 8 or 6 to find the upper bound. He would then find that all the possible solutions are between -4 and 6.
Rational Root Theorem gives you the list of 20 possible rational solutions to test. That could take a half hour or more, so we want to try to cut the number of possible trials down by using the upper and lower bounds.
Ive watched like 6 videos about this and I think that this is the first time I have *kind of* understood it. Thats the first step. Now Ima have to watch it again to pound it into my brain. Thanks for this!
Kamran Karimi he just guessed to reduce the possibilities of finding a zero maybe? he now knows that zeroes are between those 2 numbers... or the charts he had were an example of the polynomial in his classroom
Thank you for posting this helpful videos.. These Common Core books make Nooo Effin sense but Mr Berger knows how to clear things up the ole fasion way
I have a harder one im working on now and this helped a lot but what about when you have rational zeros for the factors of 42 and 4? Theres so many numbers to try it too long! Any help on a shortcut?
I thought you had to use the factors of the constant term over the factors of the leading coefficient? -4 is a factor but 5 is not. I am in a course online and use pearson it is the worst thing ever. It pretty much said to use the terms that give you a real zero, so when i got to a question that didnt have a real zero from the factors i got it wrong. Pearson didnt explain that the upperbound is the lowest number that will give you all positives when using synthetic division not requiring it to be a real zero. look i did it in one sentence but pearson couldnt figure out how to do it in a 6 minute video.
You're right. You wouldn't have tested for 5. A student would have tested with 6, because 5 is not a factor of 48. So, as you're testing for 0's, you want to notice the pattern of the answers in your synthetic division to find the upper and lower boundaries. Also, once you find your upper boundary, you don't have to test for 0's at higher numbers. This will stop you from testing 8, 12, 24, and 48, since they are also factors of 48, but are outside of the upper bound. Hope that helps
Dear Professor, how do I find the upper bound of this function y= 70 - 5^2 where x,y > 0. x = 3.74 and x = -3.74 are the points where y = 0. With synthetic division method do we need all the result values to be positive to define the upper bound. In this function all the results have any negative value beacause of -5. 4| -5 0 70 -20 -10 Can you please asnwer to this question? Will the bounds be 3.74 and - 3.74 in this case?
Apparently it has been proven that there cannot be a formula developed (like the quadratic formula) to find the roots of polynomials degree 3 and greater. Too bad.
Can u tell me why u used 5? B cuz it is not a factor of lowest term (48÷1). Shouldnt we use the factors we found from the ratio of constant term and coefficient of leading term??
I've been wasting my life watching ripvine compilations, people doing stupid shit, people saying stupid shit and the fact that I haven't been watching these videos to help my grades really make me disappointed in myself.
What does it mean if I got all negative numbers for my synthetic division? I am working on another problem by the way so this may not be applicable to the video.
I'm guessing we would need to guess the -4 and 5 if we wanted to find the domain of the zeros? And also, I assume that if it is alternating - and + signs, it is the minimum and if they are all positive ( or maybe all negative?) then we have found the maximum a zero can be? Would anyone care to clarify if they know? Thanks!
