Student Video #1
This video covers how to find all zeroes to a polynomial of 4th degree. It will start by finding all the possibilities of the coefficient and the leading degree. Of course, there were a lot of possibilities, so we narrowed down the possibilities by using Descartes Rule of Signs. That narrowed down our possibilities and we then went straight into trial-and-error with the different zeroes using synthetic division. After bringing down the equation to a quadratic equation, we used the quadratic formula to find the remaining zeroes. We carefully solved the equation and set them x-(...) to find the exact zeroes.
The viewer has to note that the odd degree changes signs, but that the even degree does not, just as it was mentioned in the video. Along with that, one must acknowledge that not all the possibilities work and that a only a process of trial- and-error will help lead to the quadratic equation. Also, remember that the the radical cannot be left as a negative, so there will be imaginary numbers. This goes back to the reason why we tend to count down by 2's during Descartes Rule of Sign. Lastly, the factors can be written as a quadratic equation, but it can also be left as the answer one gets after completing the quadratic formula.
*Here's a correction, sorry about the mistake.
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