SOLUTION: Find a third�degree polynomial function such that f(0) = 18 and whose zeros are �1, 2, and 3. Using complete sentences, explain how you found it.

Question 467453: Find a third�degree polynomial function such that f(0) = 18 and whose zeros are �1, 2, and 3. Using complete sentences, explain how you found it.

Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
-1 a root means x + 1 is a factor of the polynomial
2 a root means x - 2 is a factor of the polynomial
3 a root means x - 3 is a factor of the polynomial
==> The polynomial is of the form f(x) = a(x+1)(x-2)(x-3), where a is an undetermined coefficient. To find the value of c, use the boundary condition f(0) = 18.
==> f(0) = c(0+1)(0-2)(0-3) = c*1*-2*-3 = 6c = 18 ==> c = 3.
Hence the polynomial is f(x) = 3(x+1)(x-2)(x-3). I leave it up to you to multiply out the linear factors.
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