The polynomial generated from the given zeros is: $ P(x) = x^6-27x^5+265x^4-1245x^3+2974x^2-3408x+1440 $
Step 1: Turn the zeros into factors:
Zero | Factor |
$ 1 $ | $ x-1 $ |
$ 2 $ | $ x-2 $ |
$ 3 $ | $ x-3 $ |
$ 4 $ | $ x-4 $ |
$ 5 $ | $ x-5 $ |
$ 12 $ | $ x-12 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-1 \right) \cdot \left( x-2 \right) \cdot \left( x-3 \right) \cdot \left( x-4 \right) \cdot \left( x-5 \right) \cdot \left( x-12 \right) = x^6-27x^5+265x^4-1245x^3+2974x^2-3408x+1440 $$