The polynomial generated from the given zeros is: $ P(x) = 4x^3-13x^2-13x+4 $
Step 1: Turn the zeros into factors:
Zero | Factor |
$ -1 $ | $ x+1 $ |
$ \dfrac{ 1 }{ 4 } $ | $ 4x-1 $ |
$ 4 $ | $ x-4 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x+1 \right) \cdot \left( 4x-1 \right) \cdot \left( x-4 \right) = 4x^3-13x^2-13x+4 $$