Question

What is the polynomial function of least degree whose only zeros are -3, -2, 4?

a) F(x) = (x + 3)(x + 2)(x - 4)
b) F(x) = (x - 3)(x + 2)(x - 4)
c) F(x) = (x - 3)(x + 2)(x + 4)
d) F(x) = (x + 3)(x - 2)(x + 4)

Answer 1

The polynomial function with zeros at -3, -2, 4 is F(x) = (x + 3)(x + 2)(x - 4).

Step-by-step explanation:

The polynomial function of least degree whose only zeros are -3, -2, 4 is F(x) = (x + 3)(x + 2)(x - 4). This function is obtained by setting each zero as an individual factor such that when x equals the zero, the factor equals zero. Substituting these values into the form (x - zero), we get the corresponding factors and their signs are determined by the fact that we need the factor to be zero when x equals the given zero. Hence, a zero at x = -3 yields the factor (x + 3), a zero at x = -2 gives us (x + 2), and a zero at x = 4 results in (x - 4).