46. Find an equation for a polynomial that satisfies the given conditions. Is there more than one answer for each set of conditions? If so, give another polynomial. If not, explain why. (a) A degree 46 polynomial f(x) with zeros only at x = 3, x = -2, and x = 4 with lim ƒ(x) = − ∞ and lim f(x) = = ∞. Answer: f(x) = -(x − 3)²(x − 4)(x + 2). There is more than one answer. Find another. (b) A degree 5 polynomial g(x) with zeros at x = 3, x = 0, x = -1, and a double zero at x = -5 such that lim g(x) = -∞. Answer: f(x) = x(x − 3)(x + 1)(x + 5)². There is more than one answer. Find another. (c) A degree 4 polynomial h(x) with zeros at x = 3, x = 2, and a double zero at x = 0 that passes through the point (8, -3). Answer: f(x) = x²(x + 1)(x − 1)(x + 2)2. There is only one answer. Explain why.