How do you write a polynomial in standard form given the zeros x=3,1,2,and-3?

1 Answer
May 24, 2016

Answer:

#f(x) = x^4-3x^3-7x^2+27x-18#

Explanation:

The simplest polynomial with these zeros is:

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

#= (x^2-9)(x^2-3x+2)#

#= x^4-3x^3-7x^2+27x-18#

Standard form has one term of each degree in descending order of degree (omitting any terms with #0# coefficient).

Any polynomial in #x# with these zeros will be a multiple (scalar or polynomial) of this #f(x)#.