A limit is a point on a graph that we look at from the left and the right and we see the numbers approaching the point on the graph we looked at. We know if limits exist by looking at the right hand of the number and the left hand and see if they approach the same number. Limits help us explain function behavior at points of discontinuity by showing what happens at the right side and the left side at the point of discontinuity.
In this worksheet, we did problems on finding zeros by factoring, graphing, long division, and synthetic dividing. The connection between zeros and factors is that they are opposites. With factors you can find the zeros and with zeros you can find the factors. Division helps us use to factor polynomials because we use the quadratic formula to find the zeros we need. If we have three variables long division and synthetic division will help us find those. The degree of the polynomial helps us find the number of zeros in the formula. For example, if you had something like x^4-4x^3+8x^2-16x+32 you can tell that we will be looking for 4 zeros. This will always tell us how many zeros we will have, even if you have repeating numbers. It will never change.
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March 2015
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