In this Student Problem we are first reviewing how to create a polynomial expression starting with the zeroes and their multiplicity. This is labeled 1 with a circle around it in the picture above. Then, the following step are numbered as well up until six. All the steps shown are taken to learn how to use information known to graph a polynomial. This information includes: how to find factors based on zeroes, how to multiply factors, how to interpret end behavior, how to solve for your y-intercept, and finally how to use the multiplicity number to know whether the line of a graph goes through, bounces, or curves.
In order to complete this student problem correctly you must remember that the zeroes are opposite of the factors so it will always be (x minus "zero"). Another key thing you must remember is how to know whether a line goes through, bounces, or curves using the multiplicity number. Mrs. Kirch's catchy tune of "1,2,3, TBC" is a good way to remember. If the multiplicity is 1, then the line goes Through, if it is 2 then the line Bounces, and if it is 3 the line Curves.
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