Use the rational zeros theorem to list all possible zeros of the function $f(x)=7 x^{3}-3 x^{2}-x+2$ Enter the possible zeros separated by commas. You do not need to factor the polynomial.
Answer
\(\boxed{\text{The possible rational zeros of the function } f(x)=7 x^{3}-3 x^{2}-x+2 \text{ are } \pm1, \pm2, \pm\frac{1}{7}, \pm\frac{2}{7}}\)
Step 1 ：Given the function \(f(x)=7 x^{3}-3 x^{2}-x+2\).
Step 2 ：We use the Rational Root Theorem which states that if a polynomial has a rational root, then it must be a factor of the constant term divided by a factor of the leading coefficient.
Step 3 ：In this case, the constant term is 2 and the leading coefficient is 7.
Step 4 ：The factors of 2 are 1 and 2, and the factors of 7 are 1 and 7.
Step 5 ：Therefore, the possible rational roots are \(\pm1, \pm2, \pm\frac{1}{7}, \pm\frac{2}{7}\).
Step 6 ：\(\boxed{\text{The possible rational zeros of the function } f(x)=7 x^{3}-3 x^{2}-x+2 \text{ are } \pm1, \pm2, \pm\frac{1}{7}, \pm\frac{2}{7}}\)
