The polynomial generated from the given zeros is: $ P(x) = 10x^3-11x^2-x+2 $
Step 1: Turn the zeros into factors:
Zero | Factor |
$ -\dfrac{ 2 }{ 5 } $ | $ 5x+2 $ |
$ 1 $ | $ x-1 $ |
$ \dfrac{ 1 }{ 2 } $ | $ 2x-1 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( 5x+2 \right) \cdot \left( x-1 \right) \cdot \left( 2x-1 \right) = 10x^3-11x^2-x+2 $$