Question 275639
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If *[tex \Large a] is a zero of a polynomial function, then *[tex \Large x\ -\ a] is a factor of the polynomial.


Therefore, *[tex \Large x\ -\ \frac{1}{2}], *[tex \Large x\ -\ 5], and *[tex \Large x\ +\ 2] are the factors of your desired simplest polynomial.  All you need to do is multiply the three binomials together to get a single 3rd degree polynomial.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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