Question

Use the rational zeros theorem to list the potential zeros of

f(x)=−25x⁵ −x⁴ x5
a) ±1,±5,±25
b) ±1,±2,±4,±5,±8,±10,±20,±25
c) ±1,±3,±5,±15,±25
d) ±1,±5

Answer 1

The potential rational zeros of the polynomial f(x)=−25x⁵ −x⁴ + xµ are ±1, ±5, ±25, which are found by applying the rational zeros theorem, dividing factors of the constant term by factors of the leading coefficient.

Step-by-step explanation:

The rational zeros theorem states that if a polynomial function with integer coefficients has rational zeros, then each zero can be expressed in the form ±p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.

For the polynomial function f(x) = −25x⁵ −x⁴ + xµ, the constant term is 1 (ignoring typos in the question), and the leading coefficient is −25.

To find the potential rational zeros, we list the factors of the constant term (p = ±1) and divide by the factors of the leading coefficient (q = ±1, ±5, ±25), yielding the potential zeros: ±1, ±5, ±25.