Question

Determine an equation of a polynomial function of the lowest degree with integer coefficients that has x-intercepts of 1, -2, and -3.

Answer 1

To find an equation of a polynomial function with x-intercepts of 1, -2, and -3, we can use the factored form of a polynomial equation. The equation is f(x) = (x - 1)(x + 2)(x + 3), which expands to f(x) = x^3 + 4x^2 - 5x - 6.

Step-by-step explanation:

To determine an equation of a polynomial function with x-intercepts of 1, -2, and -3, we can start by using the factored form of a polynomial equation. Since the x-intercepts are given, we know that the factors are (x - 1), (x + 2), and (x + 3). Multiplying these factors together, we get the polynomial function:

f(x) = (x - 1)(x + 2)(x + 3)

Expanding this equation gives:

f(x) = x3 + 4x2 - 5x - 6