The polynomial generated from the given zeros is: $ P(x) = x^4-552x^3+77908x^2-1245840x+2184448 $
Step 1: Turn the zeros into factors:
Zero | Factor |
$ 2 $ | $ x-2 $ |
$ 16 $ | $ x-16 $ |
$ 212 $ | $ x-212 $ |
$ 322 $ | $ x-322 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-2 \right) \cdot \left( x-16 \right) \cdot \left( x-212 \right) \cdot \left( x-322 \right) = x^4-552x^3+77908x^2-1245840x+2184448 $$