Final answer:
No, neither the Remainder Theorem nor the Rational Zeros Theorem can be used to factor any polynomial. The Remainder Theorem helps find a remainder, not factors, and the Rational Zeros Theorem is limited to identifying possible rational zeros, which may not exist for all polynomials.
Step-by-step explanation:
The correct answer is b) No, neither the Remainder Theorem nor the Rational Zeros Theorem can be used to factor any polynomial. The Remainder Theorem can help us find the remainder when a polynomial is divided by a binomial of the form (x - c), which can be useful in the factoring process if the remainder is zero, indicating that (x - c) is a factor. However, the theorem itself does not factor polynomials. The Rational Zeros Theorem provides a list of possible rational zeros of a polynomial function based on its coefficients. It is very useful for identifying the rational zeros, and if there are any, they can be used to factor the polynomial. But if a polynomial does not have rational zeros, or if it has irrational or complex roots, this theorem cannot be used to factor it completely. Moreover, some polynomials are not factorable over the rational numbers at all, for instance, prime polynomials. These are polynomials that cannot be factored into the product of two non-constant polynomials with rational coefficients, showing that the Rational Zeros Theorem has limitations.