The polynomial generated from the given zeros is: $ P(x) = x^4-57x^3+1161x^2-9707x+26010 $
Step 1: Turn the zeros into factors:
Zero | Factor |
$ 5 $ | $ x-5 $ |
$ 17 $ | $ x-17 $ |
$ 17 $ | $ x-17 $ |
$ 18 $ | $ x-18 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-5 \right) \cdot \left( x-17 \right) \cdot \left( x-17 \right) \cdot \left( x-18 \right) = x^4-57x^3+1161x^2-9707x+26010 $$