if f(x) is a cubic polynomial, find a rule for f (x)

Question

may be left in factored form

Answer 1

A general cubic polynomial function can be written as f(x) = a x^3 + b x^2 + c x + d.

The Factor Theorem, a corollary of The Fundamental Theorem of Algebra, says that f can also be written in factored form as f(x) = a (x-r_1) (x-r_2) (x-r_3) where the roots/zeros, r_i, are complex.

 

If the zeros are known, substitute them into the factored form.