The polynomial generated from the given zeros is: $ P(x) = 15x^3-13x^2-3x+1 $
Step 1: Turn the zeros into factors:
Zero | Factor |
$ \dfrac{ 1 }{ 5 } $ | $ 5x-1 $ |
$ -\dfrac{ 1 }{ 3 } $ | $ 3x+1 $ |
$ 1 $ | $ x-1 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( 5x-1 \right) \cdot \left( 3x+1 \right) \cdot \left( x-1 \right) = 15x^3-13x^2-3x+1 $$