Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms.
Second-degree, with zeros of −2 and 4, and goes to −∞ as x→−∞.

The polynomial function p(x) of second degree, having zeroes (-2 and 4) and going to (-∞) as [x → (-∞)] will be (-x² + 2x + 8).As per the question statement, we are required to construct a polynomial [p(x)] of second degree, whose zeroes are (-2 and 4) and goes to (∞) as [x → ∞].To solve this question, first we need to understand what "Zeroes of a Polynomial" mean.The input values to the variable of a polynomial, which produces an output of (0) magnitude, or in simpler terms, those values which when substituted for the variable terms of an equation, the magnitude of the equation becomes zero, are known as the zeroes of that polynomial.And if "m" and "n" are the zeroes of a polynomial function of variable "x", then (x - m) and (x - n) will be two factors of the equation.Here, since our concerned polynomial function p(x) has zeroes of              (-2 and 4), therefore, [x - (-2)] and (x - 4) will be two factors of p(x),Or, [{(x + 2)(x - 4)} = p(x)]Or, [p(x) = (x² - 4x + 2x - 8)]Or, [p(x) = (x² - 2x - 8)]Now, (x² - 2x - 8) is a second degree polynomial, and since our concerned polynomial function p(x) is also of second degree, (x² - 2x - 8) matches the second criteria.Finally, we know that all second degree polynomials are equations for parabolas, and (x² - 2x - 8) represents a parabola that opens upwards, as it goes to (+∞), but the third and last criteria of p(x) is going to (-∞) as       [x → (-∞)], therefore, we will have to consider a negative of (x² - 2x - 8), which will represent a a parabola that opens downwards.Therefore, our required polynomial function p(x) is [-(x² - 2x - 8)]                                                                                  = (-x² + 2x + 8)To learn more about Polynomial Functions, click on the link below.https://brainly.com/question/25244466#SPJ9