Use the rational zeros theorem to list all possible rational zeros of the following. $$ h(x)=10 x^{3}+4 x^{2}-6 x+5 $$ Be sure that no value in your list appears more than once.

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1. Identify the constant term and the leading coefficient of the polynomial  
   $$
   h(x)=10x^3+4x^2-6x+5.
   $$
   The constant term is $$5$$ and the leading coefficient is $$10$$.

2. List the factors of the constant term $$5$$:  
   $$
   \pm 1, \quad \pm 5.
   $$

3. List the factors of the leading coefficient $$10$$:  
   $$
   \pm 1, \quad \pm 2, \quad \pm 5, \quad \pm 10.
   $$

4. According to the Rational Zeros Theorem, any rational zero of the polynomial is of the form  
   $$
   \frac{p}{q},
   $$
   where $$p$$ is a factor of the constant term and $$q$$ is a factor of the leading coefficient.

5. Form all possible fractions $$\frac{p}{q}$$ using the factors from steps 2 and 3:
   - With $$p = \pm 1$$:
     $$
     \pm \frac{1}{1}=\pm 1,\quad \pm\frac{1}{2},\quad \pm\frac{1}{5},\quad \pm\frac{1}{10}.
     $$
   - With $$p = \pm 5$$:
     $$
     \pm \frac{5}{1}=\pm 5,\quad \pm\frac{5}{2},\quad \pm\frac{5}{5}=\pm 1,\quad \pm\frac{5}{10}=\pm \frac{1}{2}.
     $$

6. Remove any repeated values to obtain the final list of distinct possibilities:
   $$
   \pm 1,\quad \pm 5,\quad \pm \frac{1}{2},\quad \pm \frac{5}{2},\quad \pm \frac{1}{5},\quad \pm \frac{1}{10}.
   $$
The possible rational zeros are $$ \pm1, \pm5, \pm\frac{1}{2}, \pm\frac{5}{2}, \pm\frac{1}{5}, \pm\frac{1}{10} $$.

Use the rational zeros theorem to list all possible rational zeros of the following.

Be sure that no value in your list appears more than once.

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Use the rational zeros theorem to list all possible rational zeros of the following. Be sure that no value in your list appears more than once.