The polynomial generated from the given zeros is: $ P(x) = 100x^5-2100x^4-13571x^3+15018x^2-4484x+312 $
Step 1: Turn the zeros into factors:
Zero | Factor |
$ \dfrac{ 1 }{ 10 } $ | $ 10x-1 $ |
$ \dfrac{ 1 }{ 2 } $ | $ 2x-1 $ |
$ \dfrac{ 2 }{ 5 } $ | $ 5x-2 $ |
$ -6 $ | $ x+6 $ |
$ 26 $ | $ x-26 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( 10x-1 \right) \cdot \left( 2x-1 \right) \cdot \left( 5x-2 \right) \cdot \left( x+6 \right) \cdot \left( x-26 \right) = 100x^5-2100x^4-13571x^3+15018x^2-4484x+312 $$