The polynomial generated from the given zeros is: $ P(x) = 2x^4-21x^3+64x^2-63x+18 $
Step 1: Turn the zeros into factors:
Zero | Factor |
$ \dfrac{ 1 }{ 2 } $ | $ 2x-1 $ |
$ 1 $ | $ x-1 $ |
$ 3 $ | $ x-3 $ |
$ 6 $ | $ x-6 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( 2x-1 \right) \cdot \left( x-1 \right) \cdot \left( x-3 \right) \cdot \left( x-6 \right) = 2x^4-21x^3+64x^2-63x+18 $$