How do you write a polynomial in standard form given the zeros x=-3,-2,0,2 ?

1 Answer
Jun 9, 2016

x^4+3x^3-4x^2-12x

Explanation:

The standard form of a polynomial is when the polynomial is written as a sum of decreasing power of the variable, in this case x. The question has given us the information to write the factored version of the polynomial where it has been set equal to zero, i.e.:

(x+3)(x+2)(x)(x-2)=0

To get our polynomial in standard form, we need to multiply the factors out.

(x^2+5x+6)(x)(x-2)=0

(x^3+5x^2+6x)(x-2)=0

x^4+3x^3-4x^2-12x=0

so the standard form for our polynomial is

x^4+3x^3-4x^2-12x