The polynomial generated from the given zeros is: $ P(x) = x^5-30x^4+330x^3-1640x^2+3669x-2970 $
Step 1: Turn the zeros into factors:
Zero | Factor |
$ 5 $ | $ x-5 $ |
$ 3 $ | $ x-3 $ |
$ 2 $ | $ x-2 $ |
$ 9 $ | $ x-9 $ |
$ 11 $ | $ x-11 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-5 \right) \cdot \left( x-3 \right) \cdot \left( x-2 \right) \cdot \left( x-9 \right) \cdot \left( x-11 \right) = x^5-30x^4+330x^3-1640x^2+3669x-2970 $$