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Answer 1 · 2017-11-30T00:35:10

Required Polynomial Function is given by
#x^3 - 7x - 6 = 0#

Since we are given Zeros of the Polynomial Function, we will convert these Zeros to factors in our first step.

Hence, we get the factors as follows:

#(x + 1) (x + 2) (x - 3) = 0#

Why are we doing this?

You must observe that since (x + 1) is a factor, then we write (x + 1) = 0, and #x = -1# which gives us ( -1 ) as a Zero for our Polynomial.

In our next step, we will multiply these Binomials to expand and to obtain the required polynomial function.

Use FOIL Method to expand our Binomials.

#(x + 1) (x + 2) (x - 3) = 0#

First we will multiply

#(x + 1) (x + 2)#

#rArr (x^2 + 2x + 1x + 2)#

#rArr (x^2 + 3x + 2)#

Next we will multiply

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

#rArr (x^3 + 3x^2 + 2x - 3x^2 - 9x -6)#

#rArr (x^3 - 7x -6)#

Hence, our required Polynomial Function is

# (x^3 - 7x -6) = 0#