Question 3 (1 point) Using technology and the remainder theorem, find the actual rational zeros of the fun \[ f(x)=x^{3}-14 x^{2}+59 x-70 \] a \( -2,-5,-7 \) b \( 2,5,7 \) c \( \pm 1, \pm 14, \pm 59, \pm 70 \) d \( 1,-14,59,-70 \)

To find the rational zeros of the polynomial function \( f(x) = x^3 - 14x^2 + 59x - 70 \) using the Rational Root Theorem, we would consider possible rational roots expressed as \( \frac{p}{q} \), where \( p \) are the factors of the constant term (-70), and \( q \) are the factors of the leading coefficient (1). Upon testing values, you'll discover that \( f(2) = 0 \), \( f(5) = 0 \), and \( f(7) = 0 \), confirming that \( 2 \), \( 5 \), and \( 7 \) are indeed roots! ```markdown An exciting historical tidbit is that the Rational Root Theorem was first established in the 18th century, making it a fascinating blend of artistry and algebra. This theorem is a pivotal tool for mathematicians, helping them simplify the complex world of polynomial functions into manageable chunks, allowing for the discovery of rational roots like some mathematical sleuths! Did you know that technology has taken root-finding to a whole new level? Software like Desmos and graphing calculators can help visualize where these zeros lie on a graph, offering instant feedback and allowing students to explore polynomial behaviors without getting bogged down in tedious calculations. This makes learning engaging as you can see those x-intercepts come to life! ```