The polynomial generated from the given zeros is: $ P(x) = 2x^4+x^3-25x^2+12x $
Step 1: Turn the zeros into factors:
Zero | Factor |
$ 0 $ | $ x $ |
$ \dfrac{ 1 }{ 2 } $ | $ 2x-1 $ |
$ 3 $ | $ x-3 $ |
$ -4 $ | $ x+4 $ |
Step 2: Multiply the factors together:
$$ P(x) = x \cdot \left( 2x-1 \right) \cdot \left( x-3 \right) \cdot \left( x+4 \right) = 2x^4+x^3-25x^2+12x $$