The polynomial generated from the given zeros is: $ P(x) = x^5-65x^4+1548x^3-16880x^2+83776x-152880 $
Step 1: Turn the zeros into factors:
Zero | Factor |
$ 14 $ | $ x-14 $ |
$ 5 $ | $ x-5 $ |
$ 14 $ | $ x-14 $ |
$ 6 $ | $ x-6 $ |
$ 26 $ | $ x-26 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-14 \right) \cdot \left( x-5 \right) \cdot \left( x-14 \right) \cdot \left( x-6 \right) \cdot \left( x-26 \right) = x^5-65x^4+1548x^3-16880x^2+83776x-152880 $$