What are the rational zeros of f(x)=x^3-13x^2+47x-35 Choose the possible rational zeros for f(x)=x^3-13x^2+47x-35 A. 1,5,7 B. 1,5,7,35 C. pm 1,pm 5,pm 7,pm 35 D. pm 1,pm 5,pm 7

To find the rational zeros of the polynomial \( f(x) = x^3 - 13x^2 + 47x - 35 \), we can use the Rational Root Theorem. This theorem states that any rational zero, expressed as a fraction \( \frac{p}{q} \), must have \( p \) as a factor of the constant term and \( q \) as a factor of the leading coefficient.<br /><br />For the polynomial \( f(x) = x^3 - 13x^2 + 47x - 35 \):<br />- The constant term is \(-35\).<br />- The leading coefficient is \(1\).<br /><br />The factors of \(-35\) (constant term) are:<br />\[ \pm 1, \pm 5, \pm 7, \pm 35 \]<br /><br />The factors of \(1\) (leading coefficient) are:<br />\[ \pm 1 \]<br /><br />Thus, the possible rational zeros are:<br />\[ \pm 1, \pm 5, \pm 7, \pm 35 \]<br /><br />Therefore, the correct answer is:<br />C. \( \pm 1, \pm 5, \pm 7, \pm 35 \)