SOLUTION: Write a 3rd degree polynomial function that has zeros at x= -2, 4, 6 and also passes though the point (0,3 0

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Write a 3rd degree polynomial function that has zeros at x= -2, 4, 6 and also passes though the point (0,3 0      Log On


   

Question 880364: Write a 3rd degree polynomial function that has zeros at x= -2, 4, 6 and also passes though the point (0,3
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Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
A 3rd degree polynomial with zeros at x=-2 , x=4 , and x=6 ,
must have the factoring p%28x%29=a%28x-%28-2%29%29%28x-4%29%28x-6%29=a%28x%2B2%29%28x-4%29%28x-6%29 .
If it "passes though the point (0,3)", then
p%280%29=3 , so
a%280%2B2%29%28x-4%29%28x-6%29=3--->2%28-4%29-6%29a=3--->48a=3--->a=3%2F48-->a=1%2F6 .
So the polynomial is
p%28x%29=%281%2F16%29%28x%2B2%29%28x-4%29%28x-6%29 .