The polynomial generated from the given zeros is: $ P(x) = 125x^4-575x^3+705x^2-333x+54 $
Step 1: Turn the zeros into factors:
Zero | Factor |
$ 3 $ | $ x-3 $ |
$ \dfrac{ 3 }{ 5 } $ | $ 5x-3 $ |
$ \dfrac{ 3 }{ 5 } $ | $ 5x-3 $ |
$ \dfrac{ 2 }{ 5 } $ | $ 5x-2 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-3 \right) \cdot \left( 5x-3 \right) \cdot \left( 5x-3 \right) \cdot \left( 5x-2 \right) = 125x^4-575x^3+705x^2-333x+54 $$