Answer:
x^3 + 5x^2 + 2x - 8.
Explanation:
To find the equation of a polynomial function, we need to know the roots and the degree of the function. We are given the roots -4, -2, and 1.
Since these are the roots, we know that the factors of the polynomial are (x + 4), (x + 2), and (x - 1). We can find the equation by multiplying these factors together:
(x + 4)(x + 2)(x - 1)
To simplify this expression, we can use FOIL (First, Outer, Inner, Last) method:
(x + 4)(x + 2)(x - 1) = (x^2 + 2x + 4x + 8)(x - 1) = (x^2 + 6x + 8)(x - 1)
Expanding further, we get:
(x^2 + 6x + 8)(x - 1) = x^3 + 6x^2 + 8x - x^2 - 6x - 8 = x^3 + 5x^2 + 2x - 8
Therefore, the equation is:
x^3 + 5x^2 + 2x - 8.