The polynomial generated from the given zeros is: $ P(x) = x^5-8x^4+50x^2-x-42 $
Step 1: Turn the zeros into factors:
Zero | Factor |
$ -2 $ | $ x+2 $ |
$ 3 $ | $ x-3 $ |
$ 1 $ | $ x-1 $ |
$ -1 $ | $ x+1 $ |
$ 7 $ | $ x-7 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x+2 \right) \cdot \left( x-3 \right) \cdot \left( x-1 \right) \cdot \left( x+1 \right) \cdot \left( x-7 \right) = x^5-8x^4+50x^2-x-42 $$