Question 187079
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 21 (the last coefficient):


*[Tex \LARGE p=\pm1, \pm3, \pm7, \pm21]


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{3}{1}, \frac{7}{1}, \frac{21}{1}, \frac{-1}{1}, \frac{-3}{1}, \frac{-7}{1}, \frac{-21}{1}]







Now simplify


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


*[Tex \LARGE  1, 3, 7, 21, -1, -3, -7, -21]



Note: these are all of the <b>possible roots</b>. To find the actual rational roots (if there are any), you need to plug each possible root into the given polynomial. If you get a result of 0, then the corresponding input is a zero.