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When finding the zeros of a function the trick is to factor the function. To factor you divide out numbers or variables that you know are the least common multiple (LCM) you can do this by graphing the function and finding the "easy zeros" or by seeing a common variable such as 3x-9 a three can be factored out because both variables contain a three, there for the completely factored function would be: 3(x-3). Although it looks like I just pulled out the three from both sides what really happened was I divided 3 out of the equation 0=3x+9 to make 0/3=x+3 and then you move the three back over to make 0=3(x+3) Although in the previous example it was obvious that both variables had a three in common some are less common and that is why it is helpful to graph more complex functions. After graphing the functions you can find the easy zeros, these are zeros that are nice whole numbers. If I were to graph a function and I got a zero of -3 then I would know one of the factors of the function is (x+3), the signs to answer the question "what would make -3 turn equal 0?". When looking at a polynomial that is put to a power, that power is able to tell us how many x intercepts we are expected to find. But be careful some intercepts are imaginary numbers, or appear twice. If a an x-intercept is also a maximum or a minimum it tells us that the x-intercept is a repeated factor. For a maximum or minimum the polynomial was raised to an even power. Although the power does not always show us how many factors the polynomial will have because
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AuthorLindsay is in Math Class Archives
February 2017
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