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Answer :
The Rational Root Theorem is used to find potential rational zeros of polynomial functions by identifying factors of the constant term and leading coefficient, then forming all possible fractions p/q.
### Explanation
1. Rational Root Theorem
We will use the Rational Root Theorem to find the potential rational zeros of the given polynomials. The Rational Root Theorem states that if a polynomial $f(x) = a_n x^n + a_{n-1} x^{n-1} + ... + a_1 x + a_0$ has integer coefficients, then every rational zero of $f$ has the form $\frac{p}{q}$ where $p$ is a factor of the constant term $a_0$ and $q$ is a factor of the leading coefficient $a_n$.
### Examples
The Rational Root Theorem is useful in fields like cryptography and coding theory where finding roots of polynomials is essential for decoding messages or designing secure algorithms. It also helps in optimization problems where identifying potential solutions can narrow down the search space, making the process more efficient.
### Explanation
1. Rational Root Theorem
We will use the Rational Root Theorem to find the potential rational zeros of the given polynomials. The Rational Root Theorem states that if a polynomial $f(x) = a_n x^n + a_{n-1} x^{n-1} + ... + a_1 x + a_0$ has integer coefficients, then every rational zero of $f$ has the form $\frac{p}{q}$ where $p$ is a factor of the constant term $a_0$ and $q$ is a factor of the leading coefficient $a_n$.
### Examples
The Rational Root Theorem is useful in fields like cryptography and coding theory where finding roots of polynomials is essential for decoding messages or designing secure algorithms. It also helps in optimization problems where identifying potential solutions can narrow down the search space, making the process more efficient.
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