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Find a polynomial of degree 3 with real coefficients and zeros of -3,-1, and​ 4, for which ​f(-​2)=-18.

 Apr 9, 2020
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If a polynomial of degree 3 has zeros at -3, -1, and 4, the polynomial will have this form:

  f(x)  =  a·(x + 3)·(x + 1)·(x - 4)

Since  f(-2)  =  18, we can find the value for a by solving:

   18  =  a·(-2 + 3)·(-2 + 1)·(-2 - 4)

 

Find the value of  a  and substitute this into:

  f(x)  =  a·(x + 3)·(x + 1)·(x - 4)

 Apr 9, 2020

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