Question

1

Answer 1

Take each zero, for example, a, b, c.
Then multuply together (x - a)(x - b)(x - c)

Answer 2

This is true for a polynomial function.

Answer 3

So you just multiply it back together, like FOIL method but with 3 different expressions?

Answer 4

If you're looking for a polynomial, it needs to factor in a way that you'd be able to derive those zeros. For instance, going backwards from our usual solving technique:\[\text{Ex: } y = x^2-1 \Rightarrow (x+1)(x-1)=0 \Rightarrow x=\{-1,1\}\]We can say that if we know the roots as \(x=\{ a_1, a_2, \ldots \}\), going backwards we would have \[(x-a_1)(x-a_2)\cdots=0.\]Then, what would the polynomial be?