To find the easy zeros, graphing the polynomial function is the most effective way. The easy zeros are all whole numbers that touch the x-axis. To find all hard zeros, divide all easy zeros through the polynomial function. Depending on the highest power a variable is raised to in the function, depends on how many zeros you are looking for. For example, is the function x^4-9x^3+18x^2+32x-96 is looking for 4 zeros. After synthetically dividing you should end up with (x-4)(x-4)(x+2)(x-3). To find all four zeros, set each equal to zero; you will be left with -2, 3, 4, 4. The degree of the polynomial will always tell you how many zeros are in the polynomial, but it will not always tell you the amount of real numbers.
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April 2015
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