Question

Identify the simplest polynomial function with the given zeros.

A) P(x) = x^3 - x^2 - 14x + 24
B) P(x) = 2x^3 + x^2 - 14x + 24
C) P(x) = 2x^3 - 2x^2 - 10x - 24
D) P(x) = 3x^3 - 3x^2 - 14x + 24

Answer 1

The simplest polynomial function with the given zeros is P(x) = x^3 - x^2 - 14x + 24.

Step-by-step explanation:

The simplest polynomial function with the given zeros is the one that directly corresponds to the factors of the zeros. A polynomial function can be factored by identifying the values of x that make P(x) equal to zero.

From the given options, the only polynomial function that has the zeros x=2 and x=-3 is A) P(x) = x^3 - x^2 - 14x + 24.

Substituting x=2 and x=-3 into the function will result in P(2) = 0 and P(-3) = 0, which confirms the zeros.