Question

Use the rational zero theorem to list all the possible rational zeros for the given function x^5-4x^2+6x+5

Answer 1

The rational zero theorem states that if a polynomial function has a rational root, it will be of the form p/q, where p is a factor of the constant term (in this case, 5) and q is a factor of the leading coefficient (in this case, 1).

For the given function f(x) = x^5 - 4x^2 + 6x + 5, the possible rational zeros are the combinations of factors of 5 (±1, ±5) and factors of 1 (±1).

Therefore, the possible rational zeros are ±1, ±5.