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

1 Answer
David B.
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#

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