Use the Rational Theorem to list the possible rational roots.

f(x)=x^2+2x+1
f(x)=x^2-2x+5
f(x)=x^2+4x-5

To use the Rational Root Theorem to list the possible rational roots of a polynomial, we need to look at the coefficients of the polynomial.

The Rational Root Theorem states that if a polynomial function has a rational root p/q (where p and q are integers), then p is a factor of the constant term, and q is a factor of the leading coefficient.

Let's go through each of the given polynomials and apply the theorem:

1. f(x) = x^2 + 2x + 1
The constant term is 1, so the possible values for p are ±1.
The leading coefficient is 1, so the possible values for q are ±1.

The possible rational roots are: ±1/1 = ±1.

2. f(x) = x^2 - 2x + 5
The constant term is 5, so the possible values for p are ±1, ±5.
The leading coefficient is also 1, so the possible values for q are ±1.

The possible rational roots are: ±1/1 = ±1, ±5/1 = ±5.

3. f(x) = x^2 + 4x - 5
The constant term is -5, so the possible values for p are ±1, ±5.
The leading coefficient is 1, so the possible values for q are ±1.

The possible rational roots are: ±1/1 = ±1, ±5/1 = ±5.

Therefore, the possible rational roots for each of the given polynomials are ±1 and ±5.