SOLUTION: Find a polynomial function of least degree with integer coefficients that has the given zeros. Leave your answer in factored form. Zerosx= - 4, - 1,0,and (3/2)

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Question 1156239: Find a polynomial function of least degree with integer coefficients that has the given zeros. Leave your answer in factored form.
Zerosx= - 4, - 1,0,and (3/2)
Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
.

Such a polynomial with rational coefficients is THIS


    g(x) = %28x-%28-4%29%29%2A%28x-%28-1%29%29%2A%28x-0%29%2A%28x-+3%2F2%29 = %28x%2B4%29%2A%28x%2B1%29%2Ax%2A%28x-3%2F2%29.


To make the coefficients INTEGER numbers, multiply it by 2.  You will get then another polynomial

    f(x) = (x+4)*(x+1)*x*(2x-3).     


which is just with INTEGER coefficients and is, therefore, your  ANSWER.


Next you can make FOIL to get the polynomial in a standard form.