The polynomial generated from the given zeros is: $ P(x) = x^3-9x^2+20x-12 $
Step 1: Turn the zeros into factors:
Zero | Factor |
$ 1 $ | $ x-1 $ |
$ 2 $ | $ x-2 $ |
$ 6 $ | $ x-6 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-1 \right) \cdot \left( x-2 \right) \cdot \left( x-6 \right) = x^3-9x^2+20x-12 $$