The polynomial generated from the given zeros is: $ P(x) = x^5-90x^4+2858x^3-39120x^2+208341x-171990 $
Step 1: Turn the zeros into factors:
Zero | Factor |
$ 1 $ | $ x-1 $ |
$ 15 $ | $ x-15 $ |
$ 39 $ | $ x-39 $ |
$ 14 $ | $ x-14 $ |
$ 21 $ | $ x-21 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-1 \right) \cdot \left( x-15 \right) \cdot \left( x-39 \right) \cdot \left( x-14 \right) \cdot \left( x-21 \right) = x^5-90x^4+2858x^3-39120x^2+208341x-171990 $$