Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms.

Question

Third-degree, with zeros of, and passes through the point.

Answer 1

a, b and c are zeros

a 3rd degree polynomial through the point (d, e) is

P(x) = f(x-a)(x-b)(x-c)

e = f(d-a)(d-b)(d-c)

f = (1/e)(d-a)(d-b)(d-c) if you know the 3 zeros and the point (d,e) you can solve for f

P(x) = (1/e)(d-a)(d-b)(d-c)(x-a)(x-b)(x-c)