Polynomial Functions

Question

Find a polynomial function that has the following zeros.

A. -3, 2, 1 B. -4, 0, 1, 2 C. + 1, + square root 2

D. 0, 2, 5 E. 2, 1+ square root 3 F. + 4, 0, + square root 2

G. -2, -1, 0, 1, 2 H. 1+ square root 2, + square root 3 I. 0, -3

Answer 1

There's a correspondence between zeros of a polynomial and factors of the polynomial. If a, b and c are zeros of a polynomial, then (x-a), (x-b) and (x-c) must be factors of the polynomial.

For example, a polynomial in factored form with the zeros 1, 2 and 3 is

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

You can expand this to get

f(x) = (x² - 3x + 2)(x - 3) = x³ - 3x² + 2x - 3x² + 9x - 6 = x³ - 6x² + 11x - 6