Section 2.5 Question 48 [ATTACH=full]471[/ATTACH] We are given 3 zeros. This leads to a 4th degree equation. Why fourth degree? If x = -1 is a zero, then (x - 1) is a factor. If x = 2 is zero, then (x + 2) is a zero. If x = sqrt{2}I is a zero, then (x + 2sqrt{2}i) is a factor. f(x) = a(x - 1)(x + 2)(x - sqrt{2}i)(x + sqrt{2}i) After further simplification, I got the following: f(x) = a(x^2 + x - 2)(x^2 + 2) We are told that f(0) = 4. To find a, let x = 0 and set equation to 4. Solve for a. Doing this, I got the following: a = -1. f(x) = -(x^2 + x - 2)(x^2 + 2) f(x) = -x^4 - x^3 - 2x + 4 You say?