Question 626496
Any rational zero can be found through this equation


*[Tex \LARGE Roots=\frac{p}{q}] where p and q are the factors of the last and first coefficients



So let's list the factors of 10 (the last coefficient):


*[Tex \LARGE p=\pm1, \pm2, \pm5, \pm10]


Now let's list the factors of 1 (the first coefficient):


*[Tex \LARGE q=\pm1]


Now let's divide each factor of the last coefficient by each factor of the first coefficient



*[Tex \LARGE \frac{1}{1}, \frac{2}{1}, \frac{5}{1}, \frac{10}{1}, \frac{-1}{1}, \frac{-2}{1}, \frac{-5}{1}, \frac{-10}{1}]







Now simplify


These are all the distinct rational zeros of the function that could occur


*[Tex \LARGE  1, 2, 5, 10, -1, -2, -5, -10]


I'll let you test them all. 


To test them, either use synthetic division or plug in the value into the function. 


If the result is zero, then it's a root.


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