The polynomial generated from the given zeros is: $ P(x) = 20x^5-692x^4+2889x^3+42158x^2-26084x+2184 $
Step 1: Turn the zeros into factors:
Zero | Factor |
$ \dfrac{ 1 }{ 10 } $ | $ 10x-1 $ |
$ \dfrac{ 1 }{ 2 } $ | $ 2x-1 $ |
$ 14 $ | $ x-14 $ |
$ -6 $ | $ x+6 $ |
$ 26 $ | $ x-26 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( 10x-1 \right) \cdot \left( 2x-1 \right) \cdot \left( x-14 \right) \cdot \left( x+6 \right) \cdot \left( x-26 \right) = 20x^5-692x^4+2889x^3+42158x^2-26084x+2184 $$