Final answer:
To construct a polynomial function in standard form with zeroes at x=3, -8, and 0, we multiply the factors (x), (x-3), and (x+8) to get f(x) = x^3 + 5x^2 - 24x.
Step-by-step explanation:
To write a polynomial function in standard form with the zeroes x=3, -8, and 0, we need to convert these zeroes into factors of the polynomial. Since the polynomial has a zero of x=0, one of the factors is simply x. For the other two zeroes, we have the factors (x-3) and (x+8). Multiplying these factors together gives us the polynomial function in its factored form:
f(x) = x(x - 3)(x + 8)
To write this in standard form, we expand the factors:
f(x) = x(x2 + 5x - 24)
f(x) = x3 + 5x2 - 24x
Thus, the polynomial function in standard form with the given zeroes is:
f(x) = x3 + 5x2 - 24x