Question

List all possible rational zeros given by the Rational Zeros Theorem (but don't check to see which actually are zeros). (Enter your answers as a comma-separated list.) Q(x) = x^4− 3x^3 − 2x + 10

Answer 1

±1, ±2, ±5, ±10

Explanation:

The Rational Zeros Theorem states that all possible rational zeros of a polynomial with integer coefficients can be expressed as a ratio of a factor of the constant term to a factor of the leading coefficient.

For the polynomial Q(x) = x^4 - 3x^3 - 2x + 10,

the leading coefficient is 1 and the constant term is 10.

Therefore, the possible rational zeros are:

±1, ±2, ±5, ±10

Note that we need to consider both positive and negative factors of the constant term and leading coefficient. However, not all of these possible rational zeros will necessarily be actual zeros of the polynomial.