Question

List the set of possible rational zeros for f(x)=x^4-5x^3+8x^2-20x+16
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Answer 1

Explanation:

The possible rational zeros of a polynomial function are all the possible values of x, where x is a factor of the constant term of the function divided by a factor of the leading coefficient of the function.

For the polynomial function f(x) = x^4 - 5x^3 + 8x^2 - 20x + 16, the constant term is 16 and the leading coefficient is 1. Therefore, the possible rational zeros are all the possible values of x, where x is a factor of 16 divided by a factor of 1. That is, the possible rational zeros are:

±1, ±2, ±4, ±8, ±16

To check if any of these possible zeros are actually zeros of the function, we can use synthetic division or long division to test each one.