Question

Construct a polynomial function with zeros at 0, 2, and -4.

Answer 1

A polynomial function with zeros at 0, 2, and -4 is given by the equation f(x) = x(x - 2)(x + 4), which expands to f(x) = x^3 - 2x^2 - 4x.

Step-by-step explanation:

To construct a polynomial function with zeros at 0, 2, and -4, you need to use the fact that if x is a zero of the polynomial, then (x - zero) is a factor of that polynomial. For the zero at x = 0, the factor is simply x. For the zero at x = 2, the factor is (x - 2). For the zero at x = -4, the factor is (x + 4). Multiplying these factors together gives you the polynomial:

f(x) = x(x - 2)(x + 4)

This is equivalent to:

f(x) = x3 - 2x2 - 4x

This represents a cubic polynomial function with the given zeros.