Final answer:
A polynomial function in factored form with zeros at 1, -3, 4, and 0 is represented as x(x - 1)(x + 3)(x - 4). These factors correspond to the respective zeros when they are set equal to zero, which generates the zeros of the function.
Step-by-step explanation:
To write a polynomial function in factored form with zeros at 1, -3, 4, and 0, you need to use these zeros to create factors of the polynomial. Each zero corresponds to a factor that when set equal to zero, gives you the zero of the function. For example, if you have a zero at x = 1, the corresponding factor would be (x - 1). Similarly, for a zero at x = -3, the factor is (x + 3) because (x + 3) = 0 implies x = -3.
Since there is also a zero at x = 4, we include the factor (x - 4), and for the zero at x = 0, the factor is simply x. Thus, the polynomial in factored form that has these zeros is x(x - 1)(x + 3)(x - 4). To represent this function in standard polynomial form, you would expand these factors, however, the question specifically asks for the function in factored form.