The polynomial generated from the given zeros is: $ P(x) = 5x^3-18x^2+19x-6 $
Step 1: Turn the zeros into factors:
Zero | Factor |
$ 1 $ | $ x-1 $ |
$ 2 $ | $ x-2 $ |
$ \dfrac{ 3 }{ 5 } $ | $ 5x-3 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-1 \right) \cdot \left( x-2 \right) \cdot \left( 5x-3 \right) = 5x^3-18x^2+19x-6 $$