The connection between factors and zeros is that factors are basically zeros! What I mean by this is, if a problem's factored form is (x-3)(x+5)(x+8) the zeros would be 3, -5, and -8. By using division to help us find factors, we can break easily see what a factor is without having to guess and check multiple things. Division also makes it easy to find zeros, which, as I said, will lead you directly to the zeros. The degree of a polynomial tells how many zeros we should initially look for, but it doesn't necessarily tell us the exact amount that we will have. A problem can have repeating zeros that may or may not be accounted for in the equation. Therefore, it won't always tell us how many factors the problem has. Polynomials are a great way to know where to start, but they are not everything. You must always be careful and check your work to know for sure when you have finished with a problem and have arrived at the correct solution.
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AuthorPeri Sanderson is a Pre Calc student at MPHS Archives
November 2017
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