The polynomial generated from the given zeros is: $ P(x) = 2x^4-5x^3-14x^2+8x $
Step 1: Turn the zeros into factors:
Zero | Factor |
$ 0 $ | $ x $ |
$ \dfrac{ 1 }{ 2 } $ | $ 2x-1 $ |
$ -2 $ | $ x+2 $ |
$ 4 $ | $ x-4 $ |
Step 2: Multiply the factors together:
$$ P(x) = x \cdot \left( 2x-1 \right) \cdot \left( x+2 \right) \cdot \left( x-4 \right) = 2x^4-5x^3-14x^2+8x $$