how to solve problem

Question

Use the Rational Zero Theorem to list possible rational zeros for the polynomial function. (Enter your answers as a comma-separated list.)

P(x) = x3 + 3x^​2 - 6x - 8

Answer 1

The Rational Zero Theorem states that if a polynomial function has a rational zero, it must be of the form p/q, where p is a factor of the constant term (in this case, -8) and q is a factor of the leading coefficient (in this case, 1).

For the given polynomial function P(x) = x^3 + 3x^2 - 6x -8, the possible rational zeros are obtained by taking all the factors of -8 and dividing them by all the factors of 1.

The factors of -8 are: ±1, ±2, ±4, ±8. The factors of 1 are: ±1.

Therefore, the possible rational zeros for P(x) are: ±1, ±2, ±4, ±8