Let's solve this step by step.
Given the polynomial:
[tex]\[ n(x) = 3x^3 - x^2 - 39x + 13 \][/tex]
To find the possible rational zeros, we start by considering the Rational Root Theorem. The Rational Root Theorem states that any possible rational root of the polynomial is a fraction [tex]\( p/q \)[/tex], where:
- [tex]\( p \)[/tex] is a factor of the constant term (the coefficient of the [tex]\( x^0 \)[/tex] term).
- [tex]\( q \)[/tex] is a factor of the leading coefficient (the coefficient of the [tex]\( x^3 \)[/tex] term).
Here are the steps:
1. Identify the constant term and the leading coefficient:
- The constant term is [tex]\( 13 \)[/tex].
- The leading coefficient is [tex]\( 3 \)[/tex].
2. Find the factors of the constant term 13:
- The factors of [tex]\( 13 \)[/tex] are [tex]\( \pm 1 \)[/tex] and [tex]\( \pm 13 \)[/tex].
So, the factors of 13 are:
[tex]\[ 1, 13, -1, -13 \][/tex]
[Continue in the second part...]
