Answer :

Final answer:

The question asks for possible rational zeros of a polynomial. Using the rational root theorem, the possible rational zeros of the function f(x) = 5x⁴ + 32x² - 21 are ±1, ±1/5, ±3, ±3/5, ±7, ±7/5, ±21, ±21/5.

Explanation:

The subject of this question is Mathematics, specifically the topic of polynomial functions. To find the possible rational zeros of the function f(x) = 5x⁴ + 32x² - 21, we use the Rational Root Theorem. This theorem states that any rational root, written in lowest terms, will have a numerator that is a factor of the constant term (in this case, -21) and a denominator that is a factor of the leading coefficient (in this case, 5).

The factors of -21 are: ±1, ±3, ±7, and ±21. The factors of 5 are: ±1, and ±5. This gives us a rather large set of possible rational roots. Each one of these combinations of numerator and denominator is a possible rational root of this function.

So, we can then say that the possible rational zeros for the given function will be: ±1, ±1/5, ±3, ±3/5, ±7, ±7/5, ±21, ±21/5.

Learn more about Rational Root Theorem here:

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