Today I was working on a problem with a student using the rational root theorem to find the zeros of a function.  The function was something along the lines of f(x) = 5x^5 + 3x^2 + 2x + 5.  When testing the possible roots using synthetic division, remember to place 0's as the coefficients of the missing terms.  Notice there are no x^4 or x^3 terms in f(x). So when writing the coefficients to use with the synthetic division, write 5  0   0  3  2  5.  My student omitted these 0's and it completely threw off the problem. Hope this tip is helpful for those who have struggled with a similar problem.