Jhe function below has at least one rational zero. \[ h(x)=3 x^{3}-10 x^{2}+10 x-7 \]

Did you know that the Rational Root Theorem can be your best friend when searching for rational zeros? According to this theorem, if \( p/q \) is a rational zero of a polynomial, then \( p \) is a factor of the constant term (in this case, -7), and \( q \) is a factor of the leading coefficient (3). This gives you potential candidates like \( \pm 1, \pm 7, \pm \frac{1}{3}, \pm \frac{7}{3} \) to test in your function! Once you've identified these candidates, simply plug them into the polynomial function. A common mistake is neglecting to check all possibilities or forgetting to verify that the result is indeed zero. Remember, even if one candidate works, you may find more rational zeros, so keep trying each option until you’ve exhausted your choices!