The connection between factors and zeros are that factors are the factored form of zeros. For example, a zero could be x=2, but the factor would be (x-2). Division helps us factor the polynomials because it helps us break down the factors one by one. If you use synthetic division, you are also able to start with the easy zeros until you find the harder ones through the steps of division. The degree of the polynomial helps us to predict the number of zeros because that number is the amount of times that the line of the graph crosses the x axis. That doesn't always tell us the exact number of factors- it could be less, but it will never be more than that number. That's because the type of graph could only cross the x axis once, meaning that it wouldn't have 5 zero values if 5 was the degree. The number of zeros could be fewer, but not greater, than the degree.
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Kayla CampbellArchives
November 2017
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