The polynomial generated from the given zeros is: $ P(x) = 3x^3-8x^2-4x+16 $
Step 1: Turn the zeros into factors:
Zero | Factor |
$ 2 $ | $ x-2 $ |
$ 2 $ | $ x-2 $ |
$ -\dfrac{ 4 }{ 3 } $ | $ 3x+4 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-2 \right) \cdot \left( x-2 \right) \cdot \left( 3x+4 \right) = 3x^3-8x^2-4x+16 $$