The polynomial generated from the given zeros is: $ P(x) = 2x^8-23x^7+96x^6-179x^5+152x^4-48x^3 $
Step 1: Turn the zeros into factors:
Zero | Factor |
$ 0 $ | $ x $ |
$ 0 $ | $ x $ |
$ 0 $ | $ x $ |
$ 1 $ | $ x-1 $ |
$ 1 $ | $ x-1 $ |
$ \dfrac{ 3 }{ 2 } $ | $ 2x-3 $ |
$ 4 $ | $ x-4 $ |
$ 4 $ | $ x-4 $ |
Step 2: Multiply the factors together:
$$ P(x) = x \cdot x \cdot x \cdot \left( x-1 \right) \cdot \left( x-1 \right) \cdot \left( 2x-3 \right) \cdot \left( x-4 \right) \cdot \left( x-4 \right) = 2x^8-23x^7+96x^6-179x^5+152x^4-48x^3 $$