Use the rational root theorem to determine all possible rational roots of 5x3 + 4x2 + 4x + 10 = 0. Do not find the actual roots.

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

In the given polynomial 5x^3 + 4x^2 + 4x + 10 = 0, the constant term is 10 and the leading coefficient is 5.

The factors of 10 (constant term) are: ±1, ±2, ±5, ±10. The factors of 5 (leading coefficient) are: ±1, ±5.

So, according to the Rational Root Theorem, the possible rational roots of the given polynomial are all the ratios of the factors of 10 to the factors of 5.

Therefore, the possible rational roots are: ±1, ±2, ±5, ±10, ±1/5, ±2/5, ±1/2, ±10/5.